Integration · CAPE Integrated Mathematics

12 past-paper questions on Integration, part of Calculus, from every CAPE Integrated Mathematics paper on Quelpr.

1. 6(a)(i)3 marks· CAPE Integrated Mathematics · 2016 · Paper 2Determine the integral: int (4x + 7)^6 dx.
2. 6(a)(ii)2 marks· CAPE Integrated Mathematics · 2016 · Paper 2Determine the integral: int (5x^3 - 3x^2 + 1) dx.
3. 6(b)4 marks· CAPE Integrated Mathematics · 2016 · Paper 2Evaluate the definite integral int_0^(pi/2) (cos x + 2 sin x) dx.
4. 6(c)(i)4 marks· CAPE Integrated Mathematics · 2016 · Paper 2Show that P satisfies the equation P(t) = e^(kt + c).
5. 6(c)(ii)2 marks· CAPE Integrated Mathematics · 2016 · Paper 2When t = 0, P = 4000. Calculate the value of c.
6. 6(c)(iii)3 marks· CAPE Integrated Mathematics · 2016 · Paper 2Given that k = ln 2, determine the population size when t = 3.
7. 6(d)(ii)4 marks· CAPE Integrated Mathematics · 2016 · Paper 2Using integration, determine the area reserved for agricultural activities. Give your answer to the nearest whole number.
8. 6(a)4 marks· CAPE Integrated Mathematics · 2017 · Paper 2Determine \int \cos(5x - 3) \, dx.
9. 6(b)5 marks· CAPE Integrated Mathematics · 2017 · Paper 2Show that \int_{1}^{3} (x^{\frac{5}{2}} - 2) \, dx is approximately 9.08.
10. 6(c)(i)5 marks· CAPE Integrated Mathematics · 2017 · Paper 2A radioactive substance decays at a rate of \frac{dR}{dt} = -kR, where t is time and k is a constant. Show that R satisfies the equation R(t) = e^{-kt + c}.
11. 6(c)(ii)4 marks· CAPE Integrated Mathematics · 2017 · Paper 2If at time t = 0 the substance has an original mass of 500 mg, show that R(t) = 500e^{-kt}.
12. 6(d)7 marks· CAPE Integrated Mathematics · 2017 · Paper 2Find the area bounded by the function f(x) = \frac{4}{3}x^3 - 7.5x^2 + 10x, the x-axis and the line x = C, where C is the critical value of f(x) which corresponds to the maximum point. State your answer to three decimal…