IB Maths AA HL Sl 5 11 Definite Integrals and Areas Questions

Practise IB Mathematics HL 5.11 by applying definite integrals and areas methods to questions from the Question Bank.

Exam points

set up and evaluate a definite integral for area under a curve or between a function and its inverse over appropriate limits
use substitution or a known antiderivative to integrate expressions such as x/(x^2+2) and solve for an unknown boundary
calculate total enclosed area by splitting regions or using absolute differences when a curve crosses an axis

[Maximum number: 3]

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

A different solution of the differential equation, satisfying y=2 when $x=\frac{\pi}{4}$ ,
defines a curve C.

Find the area of R.

$\quad \int_{0}^{\frac{\pi}{2}}(\sin 2 x+3)^{\frac{1}{2}} \mathrm{~d} x$
=2.99

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