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Integration — WMA13 IAL Mathematics practice questions · Study-IAL

Subjects
Mathematics
WMA13
3.5

Integration

WMA13Topic 3.53 questions

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Integrating $e^x$ , $\frac{1}{x}$ and trig functions, and integration by recognition.

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Previous topic3.4Differentiation Next topic 3.6Numerical methods

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Questions

Multiple choice: 1
Calculation: 2
Total: 3

Sample questions

Original practice questions written in the style of the exam.

Question 15 marks
Find the exact value of $\displaystyle\int_0^{\frac{\pi}{4}} \left(\sec^2 x + 4\sin 2x\right) dx$ .
Mark scheme
- M1 $\int \sec^2 x\,dx = \tan x$ (1)
- M1 $\int \sin 2x\,dx = k\cos 2x$ (1)
Question 24 marks
Find the exact value of $\displaystyle\int_0^2 \frac{x}{x^2 + 4}\,dx$ , giving your answer in the form .

sin

2

x

d

x

=

kcos2x

A1

\tan x - 2\cos 2x

(1)

M1 Substitutes both limits and subtracts (1)

A1

(1 - 0) - (0 - 2) = 3

(1)

x

d

x

a\ln b

Mark scheme

M1 Recognises the form $k\ln(x^2 + 4)$ (1)
A1 $\tfrac{1}{2}\ln(x^2 + 4)$ (1)
M1 Substitutes limits: $\tfrac{1}{2}\ln 8 - \tfrac{1}{2}\ln 4$ (1)
A1 $\tfrac{1}{2}\ln 2$ (1)

1

ln

4