IB Maths AA HL Sl 5 5 Integration As Anti Differentiation Questions

Practise IB Mathematics HL 5.5 by applying integration as anti-differentiation methods to questions from the Question Bank.

Exam points

Integrate polynomial-type functions as anti-derivatives and verify the result by differentiation.
Use boundary conditions to determine constants, then connect anti-derivatives with definite integrals and area under a curve over stated limits.

[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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IB Maths AA HL Sl 5 5 Integration As Anti Differentiation Questions question 1