Mathematics 9709 · AS & A Level · Integration

Integration — practice question

(a)[3]

Calculate $\int \frac{4 + e^x}{2e^{2x}}\, dx$.

(b)[4]

Without a calculator, Calculate $\int_{2}^{10} \frac{1}{2x + 5}\, dx$, and give the result in the form $\ln k$.

(c)[3]

The diagram shows the curve $y = \log_{10}(x + 2)$ for $0 \leq x \leq 6$. The region enclosed by the curve together with the lines $x = 0$, $x = 6$ and $y = 0$ is labelled $R$. Use the trapezium rule with 2 strips to estimate the area of $R$, giving your answer correct to 1 decimal place.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Rewrite the integrand as $2e^{-2x}+\frac{1}{2}e^{-x}$

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