9709 · topic questions
Integration
12 past-paper questions on Integration
Use the substitution u = 1-sinx to find the exact value of ∫(from π/2 to 3π/2) (sin 2x / √(1-sinx)) dx. Give your answer in the…
Practise the full question →Hence find the exact value of ∫(from 1/√3 to 1/2) x tan⁻¹(2x)dx.
Practise the full question →It is given that ∫[from -1/3 to 6] (p(x))/(3x+2) dx = a+ln64, where a is an integer. Find the values of a and k.
Practise the full question →Find the exact value of ∫(from 0 to 0.5) x tan⁻¹(2x)dx.
Practise the full question →The shaded region is rotated completely about the x-axis. Find the exact volume of the solid produced.
Practise the full question →Use the substitution u = 2+cosx to find the exact area of the shaded region R.
Practise the full question →Hence find the exact value of ∫[from π/8 to π/4] (cos⁴θ - sin⁴θ + 4sin²θcos²θ) dθ.
Practise the full question →By using the substitution u = cosx, find the area of the region bounded by the curve, the x-axis between x = 0 and x = ¼π, and…
Practise the full question →Find the exact value of ∫ x² ln 3x dx. Give your answer in the form a lnb+c, where a and c are rational and b is an integer.
Practise the full question →Hence show that ∫(from 0 to 2√3) (x⁴+16)/(x²+4) dx = 4/3(π+4).
Practise the full question →Hence find the exact value of ∫(from 0 to π/12) 3/((3 cos2x - √3sin 2x)²) dx, simplifying your answer.
Practise the full question →Find the exact value of ∫[from 0 to 2/a] xe^(-ax) dx.
Practise the full question →
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Integration (9709) past-paper questions — marked instantly
These are real Cambridge Mathematics past-paper questions on Integration. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.
Frequently asked questions
- How many Integration questions are there for 9709?
- This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Integration. Each links straight to instant marking against the official 9709 scheme.
- How are Integration answers marked?
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- Where can I learn Integration first?
- Start with the free Mathematics lesson on Integration, then come back and drill past-paper questions under timed conditions.