OCR A-level Mathematics A · H240

Definite integration & areas

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Extreme practice · Multi-step problems within A-level pure maths. Difficulty is an editorial judgement. These questions are self-reviewed, not ranked.

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Calculator permitted. Give clear working in the answer booklet and label each part. Formulae are provided in the official question paper.

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01 · Pure · 100 marks · 2 hours
02 · Pure & statistics · 100 marks · 2 hours
03 · Pure & mechanics · 100 marks · 2 hours

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QUESTION PAPER

Mathematics · A levelPure mathematics · H240/01

Torus Maths original · OCR style

For a real constant b, define $I_b=\int_{-3}^{3}\frac{x^2+9}{1+\mathrm e^{bx}}dx$ .

(a)

Find an exact expression for I_b. Show that it does not depend on b.

[5]

(b)

Hence evaluate $\int_{-3}^{3}\frac{(x^2+9)\mathrm e^{bx}}{1+\mathrm e^{bx}}dx$ .

[2]

Question reference: ocr-a-level-extreme-16-01Report a question →

Answer booklet

Question 1 · Show your working

(a)

Answer booklet · Question 1(a)

(b)

Answer booklet · Question 1(b)

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