IB Maths AA HL 5.5 Integration as anti-differentiation Question Bank

Practise IB Mathematics SL/HL 5.5 by applying integration as anti-differentiation methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

Consider the differential equation $y \frac{\mathrm{~d} y}{\mathrm{~d} x}=\cos 2 x$ .

For which value of the constant of integration does your solution coincide with the function given in part (i)?

$\quad \sin 2 x+A \equiv(\cos x+\sin x)^{2}$ $(\cos x+\sin x)^{2}=\cos ^{2} x+2 \sin x \cos x+\sin ^{2} x$
use of $\sin 2 x \equiv 2 \sin x \cos x$ .
A=1

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SL 5.5—Integration as anti-differentiation question 1