CAIE A-Level Mathematics 1.8.3 Definite integrals

Practise evaluating definite integrals exactly, including logarithmic, trigonometric and improper forms with clear use of limits.

Exam points

apply upper and lower limits to exact antiderivatives, including logarithmic forms
handle ∞ limits by showing the disappearing term before giving the exact value
use integration by parts or identities before evaluating a definite integral

[Maximum number: 3]

The function f is defined by $\mathrm{f}(x)=\frac{2}{(x+2)^{2}}$ for x>-2.

Find $\int_{1}^{\infty} \mathrm{f}(x) \mathrm{d} x$ .

$\frac{-2}{x+2}$
B1
Integrate \mathrm{f}(x). Accept $-2(x+2)^{-1}$ . Can be unsimplified.
$0-\left(-\frac{2}{3}\right)=\frac{2}{3}$
M1 A1
Apply limit(s) to an integrated expansion. CAO for A1

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1.8.3—Definite integrals question 1