First slide

Introduction to definite integration

Question

$\int_{0}^{a} \sqrt{a^{2} - x^{2}} d x =$

Easy

A

$π a^{2}$
B

$\frac{π a^{2}}{2}$
C

$\frac{π a^{2}}{3}$
D

$\frac{π a^{2}}{4}$

Solution

${\int_{0}^{a} \sqrt{a^{2} - x^{2}} d x = [\frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2} S i n^{- 1} \frac{x}{a}]}_{0}^{a}$
$= 0 + \frac{a^{2}}{2} \times \frac{π}{2} - 0$

$= \frac{π a^{2}}{4}$

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