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Integration II · CAPE Pure Mathematics Unit 2

112 past-paper questions on Integration II, part of Complex Numbers and Calculus II, from every CAPE Pure Mathematics Unit 2 paper on Quelpr.

Practise Integration II
  1. 2(b)(i)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Express (2x + 1) / (x^2(x + 1)) in the form A/x + B/x^2 + C/(x + 1), where A, B, and C are constants.
  2. 2(b)(ii)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2005 · Paper 2Hence, evaluate the integral from 1 to 2 of (2x + 1) / (x^2(x + 1)) dx.
  3. 2(a)(i)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2Express (1 + x)/((x - 1)(x^2 + 1)) in partial fractions.
  4. 2(a)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2Hence, find int (1 + x)/((x - 1)(x^2 + 1)) dx.
  5. 2(b)(i)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2Evaluate I_1.
  6. 2(b)(ii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2Show that I_n = e - n I_(n-1).
  7. 2(b)(iii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2006 · Paper 2Hence, or otherwise, evaluate I_3, writing your answer in terms of e.
  8. 1(a)8 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Solve, for x > 0, the equation 3\log_8 x = 2\log_x 8 - 5.
  9. 2(a)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Show that for n \ge 2, \tan^n x = \tan^{n-2} x \sec^2 x - \tan^{n-2} x.
  10. 2(c)(i)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2By using the result in (a) above, show that I_n + I_{n-2} = \frac{1}{n-1}.
  11. 2(c)(ii)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2Hence evaluate I_4.
  12. 1(c)(i)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2Express in partial fractions: \frac{2x^2 - 3x + 4}{(x - 1)(x^2 + 1)}
  13. 1(c)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2Hence, find \int \frac{2x^2 - 3x + 4}{(x - 1)(x^2 + 1)} \,\mathrm{d}x.
  14. 2(b)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2The gradient at the point (x, y) on a curve is given by \frac{\mathrm{d}y}{\mathrm{d}x} = e^{4x}. Given that the curve passes through the point (0, 1), find its equation.
  15. 2(c)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2Evaluate \int_1^e x^2 \ln x \,\mathrm{d}x, writing your answer in terms of e.
  16. 2(d)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2Use the substitution v = 1 - u to find \int \frac{\mathrm{d}u}{\sqrt{1 - u}}.
  17. 2(d)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (Rest of Region) · Paper 2Hence, or otherwise, use the substitution u = \sin x to evaluate \int_0^{\pi/2} \sqrt{1 + \sin x} \,\mathrm{d}x.
  18. 1(a)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2Find the exact values of x such that e^x + 7e^{-x} = 8.
  19. 2(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2Find \int \frac{1}{x} \ln x \, \mathrm{d}x.
  20. 2(c)(i)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2Express \frac{2 + 3x - x^2}{(x - 1)(x^2 + 1)} in partial fractions.
  21. 2(c)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2008 (T&T) · Paper 2Hence, find \int \frac{2 + 3x - x^2}{(x - 1)(x^2 + 1)} \, \mathrm{d}x.
  22. 2(a)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2Sketch the region whose area is defined by the integral \int_0^1 \sqrt{1 - x^2}\, \mathrm{d}x.
  23. 2(b)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2Using FIVE vertical strips, apply the trapezium rule to show that \int_0^1 \sqrt{1 - x^2}\, \mathrm{d}x \approx 0.759.
  24. 2(c)(i)9 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2Use integration by parts to show that, if I = \int \sqrt{1 - x^2}\, \mathrm{d}x, then I = x\sqrt{1 - x^2} - I + \int \frac{1}{\sqrt{1 - x^2}}\, \mathrm{d}x.
  25. 2(c)(ii)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2Deduce that I = \frac{x\sqrt{1 - x^2} + \sin^{-1} x}{2} + c, where c is an arbitrary constant of integration.
  26. 2(c)(iii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2Hence, find \int_0^1 \sqrt{1 - x^2}\, \mathrm{d}x.
  27. 2(c)(iv)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2009 · Paper 2Use the results in Parts (b) and (c)(iii) above to find an approximation to \pi.
  28. 1(c)(i)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Determine \int \frac{4}{e^x + 1}\,\mathrm{d}x by using the substitution u = e^x.
  29. 1(c)(ii)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Determine \int \frac{4}{e^x + 1}\,\mathrm{d}x by first multiplying both the numerator and denominator of the integrand by e^{-x} before integrating.
  30. 2(a)(ii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Hence, or otherwise, derive the reduction formula I_n = x(\ln x)^n - n I_{n-1}, where I_n = \int (\ln x)^n\,\mathrm{d}x.
  31. 2(a)(iii)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2010 · Paper 2Use the reduction formula in (a)(ii) to determine \int (\ln x)^3\,\mathrm{d}x.
  32. 2(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2Find F_0(x) and F_n(0), given that 0! = 1.
  33. 2(a)(ii)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2Show that F_n(x) = F_{n-1}(x) - \frac{1}{n!} x^n e^{-x}.
  34. 2(a)(iii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2Hence, show that if M is an integer greater than 1, then e^x F_M(x) = -\left(x + \frac{x^2}{2!} + \frac{x^3}{3!} + \dots + \frac{x^M}{M!}\right) + (e^x - 1).
  35. 2(b)(i)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2Express \frac{2x^2 + 3}{(x^2 + 1)^2} in partial fractions.
  36. 2(b)(ii)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2Hence, find \int \frac{2x^2 + 3}{(x^2 + 1)^2} dx.
  37. 3(b)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2011 · Paper 2Find the constants A and B such that \frac{2 - 3x}{(1 - x)(1 - 2x)} \equiv \frac{A}{1 - x} + \frac{B}{1 - 2x}.
  38. 2(a)(i)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Express \frac{x^2 - 3x}{(x - 1)(x^2 + 1)} in partial fractions.
  39. 2(a)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Hence, find \int \frac{x^2 - 3x}{x^3 - x^2 + x - 1} \,\mathrm{d}x.
  40. 2(b)(i)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Given that \sin A \cos B - \cos A \sin B = \sin(A - B), show that \cos 3x \sin x = \sin 3x \cos x - \sin 2x.
  41. 2(b)(ii)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Prove that (m + 3) I_m = m J_{m-1} - \cos^m x \cos 3x.
  42. 2(b)(iii)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Hence, by setting m = 1, prove that 4 \int_0^{\frac{\pi}{4}} \cos x \sin 3x \,\mathrm{d}x = \int_0^{\frac{\pi}{4}} \sin 2x \,\mathrm{d}x + \frac{3}{2}.
  43. 2(b)(iv)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2012 · Paper 2Evaluate \int_0^{\frac{\pi}{4}} \sin 2x \,\mathrm{d}x.
  44. 2(a)(i)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2Determine \int \sin x \cos 2x \, dx.
  45. 2(a)(ii)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2Hence, calculate \int_0^{\frac{\pi}{2}} \sin x \cos 2x \, dx.
  46. 2(b)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2Let f(x) = x|x| = \begin{cases} x^2 &; x \ge 0 \\ -x^2 &; x < 0 \end{cases}. Use the trapezium rule with four intervals to calculate the area between f(x) and the x-axis for the domain -0.75 \le x \le 2.25.
  47. 2(c)(i)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2Show that \frac{2x^2 + 4}{(x^2 + 4)^2} = \frac{2}{x^2 + 4} - \frac{4}{(x^2 + 4)^2}.
  48. 2(c)(ii)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2013 · Paper 2Hence, find \int \frac{2x^2 + 4}{(x^2 + 4)^2} \, dx. Use the substitution x = 2\tan\theta.
  49. 2(a)(i)3 marks· CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2Show that F_n(x) = x(\ln x)^n - n F_{n-1}(x).
  50. 2(a)(ii)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2Hence, or otherwise, show that F_3(2) - F_3(1) = 2(\ln 2)^3 - 6(\ln 2)^2 + 12\ln 2 - 6.
  51. 2(b)(i)7 marks· CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2By decomposing \frac{y^2 + 2y + 1}{y^4 + 2y^2 + 1} into partial fractions, show that \frac{y^2 + 2y + 1}{y^4 + 2y^2 + 1} = \frac{1}{y^2 + 1} + \frac{2y}{(y^2 + 1)^2}.
  52. 2(b)(ii)8 marks· CAPE Pure Mathematics Unit 2 · May/June 2014 · Paper 2Hence, find \int_0^1 \frac{y^2 + 2y + 1}{y^4 + 2y^2 + 1} \, dy.
  53. Q31 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1Given that \cos 2x = 1 - 2\sin^2 x, then \int_0^{\pi} \sin^2\left(\frac{x}{4}\right) dx is
  54. Q101 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1Given that a, b, c and k are constants, then \int \frac{3}{x^2(x - 1)} dx can be expressed as
  55. Q111 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1The integral of \frac{1}{1 - \sin^2 x} with respect to x is
  56. Q121 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1The partial fractions of \frac{x + 3}{(2x + 5)(x - 1)^2} may be expressed in the form
  57. Q141 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 1\int \frac{dx}{\sqrt{1 - 9x^2}} =
  58. 2(b)(i)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Express f(x) in the form a + \frac{b}{9x^2 + 4} where a, b \in \mathbb{R}.
  59. 2(b)(ii)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Given that f(x) is symmetric about the y-axis, evaluate \int_{-2}^2 f(x)\,dx.
  60. 2(c)(i)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Show that \int h^n \ln h\,dh = \frac{h^{n+1}}{(n+1)^2} [-1 + (n+1)\ln h] + C, where -1 \ne n \in \mathbb{Z} and C \in \mathbb{R}.
  61. 2(c)(ii)2 marks· CAPE Pure Mathematics Unit 2 · May/June 2015 · Paper 2Hence, find \int \sin^2 x \cos x \ln(\sin x)\,dx.
  62. Q61 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1\int \frac{\sec^2 x}{2\tan x} \, dx =
  63. Q91 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1\int \frac{1}{x^2 + 4} \, dx =
  64. Q111 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1\int (\cos 5x \cos 3x) \, dx =
  65. Q131 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 1\int \frac{2x}{(x - 1)(x + 3)} \, dx =
  66. 2(b)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Determine the integral of e^(2x) sin(e^x) dx.
  67. 2(c)(i)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Use the trapezium rule with three equal intervals to estimate the area bounded by f and the lines y = 0, x = 2 and x = 5.
  68. 2(c)(ii)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Using partial fractions, show that f(x) = 3/(x - 1) - (2x)/(x^2 + 1).
  69. 2(c)(iii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2016 · Paper 2Hence, determine the value of the integral from 2 to 5 of f(x) dx.
  70. Q111 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1The integral of \frac{1}{1 - \sin^2 x} with respect to x is
  71. Q121 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 1\int 4e^{2x - 1} dx =
  72. 2(a)(i)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Use integration by parts to derive the reduction formula aI_n = x^n e^{ax} - nI_{n-1}, where I_n = \int x^n e^{ax} \, \mathrm{d}x.
  73. 2(a)(ii)6 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Hence, or otherwise, determine \int x^3 e^{3x} \, \mathrm{d}x.
  74. 2(b)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Calculate \int_0^1 \frac{\sin^{-1} x}{\sqrt{1 - x^2}} \, \mathrm{d}x.
  75. 2(c)(i)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Use partial fractions to show that \frac{2x^2 - x + 4}{x^3 + 4x} = \frac{1}{x} + \frac{x}{x^2 + 4} - \frac{1}{x^2 + 4}.
  76. 2(c)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2017 · Paper 2Hence, or otherwise, determine \int \frac{2x^2 - x + 4}{x^3 + 4x} \, \mathrm{d}x.
  77. Q101 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1\int \frac{1}{1 + 9x^2}\,dx is
  78. Q111 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1\int (\cos 5x \cos 3x)\,dx =
  79. Q131 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 1\int \frac{\sec^2 x}{2\tan x}\,dx =
  80. 2(a)(i)8 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2Determine the integral of x^5 cos(x^3) dx.
  81. 2(a)(ii)5 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2Determine the integral of e^(2x) / sqrt(1 - e^(4x)) dx.
  82. 2(b)(i)8 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2Use partial fractions to show that (x^4 + 1) / (x(x^2 + 1)^2) = 1/x - 2x / (x^2 + 1)^2.
  83. 2(b)(ii)4 marks· CAPE Pure Mathematics Unit 2 · May/June 2018 · Paper 2Hence, determine the integral of (x^4 + 1) / (x(x^2 + 1)^2) dx.
  84. Q111 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 1The integral of \frac{1}{1 - \sin^2 x} with respect to x is
  85. Q121 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 1\int 2x e^{-x}\,dx =
  86. Q131 mark · multiple choice· CAPE Pure Mathematics Unit 2 · May/June 2019 · Paper 1Given that a, b, c and k are constants, then \int \frac{3}{x^2(x - 1)}\,dx can be expressed as
  87. 1(c)(i)7 marks· Pure Mathematics · Unit 2 Q1 1(c)(i)Use partial fractions to show that (2x+1)/(3x²-x-2) = 3/(5(x-1)) + 1/(5(3x+2)).
  88. 1(c)(ii)4 marks· Pure Mathematics · Unit 2 Q1 1(c)(ii)Hence, or otherwise, determine ∫ (2x+1)/(3x²-x-2) dx.
  89. 2(a)8 marks· Pure Mathematics · Unit 2 Q2 2(a)Using the substitution eˣ = 3 cos θ, or otherwise, determine ∫ eˣ √(9-e²ˣ) dx.
  90. 2(a)6 marks· Pure Mathematics · Unit 2 Q2 2(a)Use integration by parts to evaluate ∫sec² x cosec² x dx.
  91. 2(a)8 marks· Pure Mathematics · Unit 2 Q2 2(a)Determine ∫ e^(2x) sin 3x dx.
  92. 2(a)(i)4 marks· Pure Mathematics · Unit 2 Q2 2(a)(i)Apply the trapezium rule with THREE equal intervals to estimate the value of ∫(from 0 to π/3) tan x dx.
  93. 2(a)(i)9 marks· Pure Mathematics · Unit 2 Q2 2(a)(i)Use partial fractions to show that x⁴ / (x⁴ - 1) = 1 + 1/(4(x-1)) - 1/(4(x+1)) - 1/(2(x²+1)).
  94. 2(a)(i)3 marks· Pure Mathematics · Unit 2 Q2 2(a)(i)Show that F_n(x) = x (ln x)ⁿ - nF_(n-1)(x).
  95. 2(a)(ii)7 marks· Pure Mathematics · Unit 2 Q2 2(a)(ii)Hence, or otherwise, show that F₂(2) - F₂(1) = 2 (ln 2)³ - 6 (ln 2)² + 12 ln 2 - 6.
  96. 2(a)(ii)4 marks· Pure Mathematics · Unit 2 Q2 2(a)(ii)Using an appropriate trigonometric identity, determine the EXACT value of ∫(from 0 to π/3) tan x dx.
  97. 2(a)(ii)6 marks· Pure Mathematics · Unit 2 Q2 2(a)(ii)Hence, or otherwise, determine ∫ x⁴ / (x⁴ - 1) dx.
  98. 2(b)9 marks· Pure Mathematics · Unit 2 Q2 2(b)Evaluate ∫ from 2 to 5 of (3x / (x² - 4x + 5)) dx.
  99. 2(b)7 marks· Pure Mathematics · Unit 2 Q2 2(b)Use the substitution u = cos^(-1)(x/2) to show that ∫(from 0 to 1) (cos^(-1)(x/2))/√(4-x^2) dx = 5π^2/72.
  100. 2(b)(i)12 marks· Pure Mathematics · Unit 2 Q2 2(b)(i)Use partial fractions to prove that (2x + 1) / (2x³ - x² + 8x - 4) = 8 / (17(2x - 1)) - (4x - 15) / (17(x² + 4)).
  101. 2(b)(i)5 marks· Pure Mathematics · Unit 2 Q2 2(b)(i)Show that if I_n = ∫ (1 - x)ⁿeᵃˣ dx for n ≥ 1, then I_n = (1 - x)ⁿeᵃˣ/a + n/a I_n-1.
  102. 2(b)(i)7 marks· Pure Mathematics · Unit 2 Q2 2(b)(i)By expressing (y² + 2y + 1) / (y⁴ + 2y² + 1) as partial fractions, show that (y² + 2y + 1) / (y⁴ + 2y² + 1) = 1 / (y² + 1) + 2y / (y² + 1)².
  103. 2(b)(ii)5 marks· Pure Mathematics · Unit 2 Q2 2(b)(ii)Hence, find ∫ (2x + 1) / (2x³ - x² + 8x - 4) dx.
  104. 2(b)(ii)5 marks· Pure Mathematics · Unit 2 Q2 2(b)(ii)Hence, determine ∫ (1 - x)²eᵃˣ dx.
  105. 2(b)(ii)8 marks· Pure Mathematics · Unit 2 Q2 2(b)(ii)Hence, or otherwise, evaluate ∫(y² + 2y + 1) / (y⁴ + 2y² + 1) dy.
  106. 2(c)10 marks· Pure Mathematics · Unit 2 Q2 2(c)Determine ∫((x + 1) / (x³ - 9x)) dx.
  107. 2(c)(i)6 marks· Pure Mathematics · Unit 2 Q2 2(c)(i)Derive the reduction formula ∫ sinⁿ x dx = -1/n sinⁿ⁻¹ x cos x + (n-1)/n ∫ sinⁿ⁻² x dx.
  108. 2(c)(i)6 marks· Pure Mathematics · Unit 2 Q2 2(c)(i)Show that I_n = (n-1)/n * I_(n-2).
  109. 2(c)(ii)4 marks· Pure Mathematics · Unit 2 Q2 2(c)(ii)Hence, or otherwise, show that ∫ sin⁶ x dx = -1/6 sin⁵ x cos x - 5/24 sin³ x cos x + 5/8 ∫ sin² x dx.
  110. 2(c)(ii)a)2 marks· Pure Mathematics · Unit 2 Q2 2(c)(ii)a)Verify that I_0 = π/2.
  111. 2(c)(ii)b)2 marks· Pure Mathematics · Unit 2 Q2 2(c)(ii)b)Hence, determine the value of I_4.
  112. 3(c)(i)3 marks· Pure Mathematics · Unit 2 Q3 3(c)(i)Determine the values of A and B such that 4/((2r+1)(2r+3)) = A/(2r+1) + B/(2r+3).

Related topics in Complex Numbers and Calculus II