Definite Integrals · CSEC Additional Mathematics

18 past-paper questions on Definite Integrals, part of Integration, from every CSEC Additional Mathematics paper on Quelpr.

1. 6(a)4 marks· Additional Mathematics Q6 6(a)Show that ∫₀^(π/4) (sin x + 4 cos x) dx = (3√2 + 2) / 2.
2. 6(a)4 marks· Additional Mathematics Q6 6(a)Evaluate ∫₂⁴ x (x² - 2) dx.
3. 6(a)6 marks· Additional Mathematics Q6 6(a)Show, using integration, that the finite area of the curve y = sin x in the first quadrant bounded by the line x = 4pi/3 is smaller than the finite region of y = cos x in the same quadrant and bounded by the same line.
4. 6(a)4 marks· Additional Mathematics Q6 6(a)Evaluate ∫(from π/6 to π/3) cos 3θ dθ.
5. 6(a)(ii)4 marks· Additional Mathematics Q6 6(a)(ii)Evaluate ∫(from 1 to 3) [(2/x²) - 3 + 2x³] dx.
6. 6(b)4 marks· Additional Mathematics Q6 6(b)Evaluate ∫₁⁴ (2√x)/x dx.
7. 6(b)4 marks· Additional Mathematics Q6 6(b)Evaluate ∫₀^(π/2) (3 sin x - 5 cos x) dx.
8. 6(ii)4 marks· Additional Mathematics Q6 6(ii)Use your result to show that ∫(from 1 to e) 4x ln x dx = e² + 1.
9. Q401 mark · multiple choice· CSEC Additional Mathematics · 2013 · Paper 1The value of a for which \int_0^a (x^2 - 5)\,dx = \frac{50}{3} is
10. Q401 mark · multiple choice· CSEC Additional Mathematics · 2014 · Paper 1The value of a for which \int_0^a (x^2 - 5)\,dx = \frac{50}{3} is
11. Q421 mark · multiple choice· CSEC Additional Mathematics · 2014 · Paper 1If X = \int_a^b f(x)\,dx and a < c < b then
12. Q401 mark · multiple choice· CSEC Additional Mathematics · 2015 · Paper 1If \int_2^a (6 + 3x)\,dx = 72, where a > 2, then a =
13. Q441 mark · multiple choice· CSEC Additional Mathematics · 2015 · Paper 1\int_1^2 (1 + x + x^2)\,dx =
14. Q401 mark · multiple choice· CSEC Additional Mathematics · 2016 · Paper 1If \int_2^a (6 + 3x)\,dx = 72, where a > 2, then a =
15. Q421 mark · multiple choice· CSEC Additional Mathematics · 2016 · Paper 1If X = \int_a^b f(x)\,dx and a < c < b then
16. Q401 mark · multiple choice· CSEC Additional Mathematics · 2018 · Paper 1\int_0^2 (3x + 4)^3 \,\mathrm{d}x =
17. Q411 mark · multiple choice· CSEC Additional Mathematics · 2018 · Paper 1The solution to \int_{-1}^1 \frac{1}{(5x - 2)^2} \,\mathrm{d}x is
18. Q441 mark · multiple choice· CSEC Additional Mathematics · May/June 2017 · Paper 1\int_1^2 (1 + x + x^2)\,dx =