First slide

Methods of integration

Question

$Evaluate \int \cos^{3} x \sqrt{\sin x} d x$

Easy

A

$= \frac{2}{3} \sin^{3 / 2} x - \frac{2}{7} \sin^{5 / 2} x + c$
B

$= \frac{2}{7} \sin^{3 / 2} x - \frac{2}{3} \sin^{7 / 2} x + c$
C

$= \frac{2}{3} \sin^{3 / 2} x - \frac{2}{7} \sin^{7 / 2} x + c$
D

$= \frac{2}{3} \sin^{7 / 2} x - \frac{2}{7} \sin^{5 / 2} x + c$

Solution

$\begin{array}{l} \begin{array}{l} \int \cos^{2} x \sqrt{\sin x} \cos x d x \\ \int (1 - \sin^{2} x) \sqrt{\sin x} \cos x d x \\ \int (\sin^{\frac{1}{2}} x - \sin^{\frac{5}{2}} x) \cos x d x \end{array} \\ \frac{\sin^{\frac{3}{2}} x}{\frac{3}{2}} - \frac{\sin^{\frac{7}{2}} x}{\frac{7}{2}} + c \\ = \frac{z^{3 / 2}}{3 / 2} - \frac{z^{7 / 2}}{7 / 2} + c = \frac{2}{3} z^{3 / 2} - \frac{2}{7} z^{7 / 2} + c \\ = \frac{2}{3} \sin^{3 / 2} x - \frac{2}{7} \sin^{7 / 2} x + c \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App