CAIE A-Level Mathematics AS 1.8.3 Definite Integrals Questions

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

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 3]

Find the exact value of $\int_{3}^{\infty} \frac{2}{x^{2}} \mathrm{~d} x$ .

Integrate to obtain $-2 x^{-1}$
OE

Substitute limits correctly with clear indication seen that upper limit gives 0
For integral of form $-k x^{-n}$ , where k>0, n>0.

Obtain $\frac{2}{3}$
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CAIE A-Level Mathematics AS 1.8.3 Definite Integrals Questions question 1