A-level · Integration

Integration by reversing the chain ruleExam-style questions

Integrating by recognition — spotting the chain rule's fingerprint, the derivative of an inside function sitting as a factor. A power of a function; adjusting the answer when the factor is a number out; the log case, when the top is the derivative of the bottom; exponential and trig insides; and how to tell when recognition fails and you need to expand or substitute.

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19 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
In this question you must show detailed reasoning.

The diagram shows the curve $y = \dfrac{6}{2x+1}$ and the line $y = 6 - 2x$ .The curve and the line intersect at the points where $x = 0$ and $x = \dfrac{5}{2}$ . The region $R$ , shaded in the diagram, is bounded by the curve and the line.

Determine the exact area of $R$ . (10 marks)
Level 5 · 10 marksTry it