Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
0 votes

$ I= \int \limits_0^{\frac{\pi}{2}} \cos ^3 x dx$

\[\begin {array} {1 1} (a)\;\frac{1}{3} \\ (b)\;1 \\ (c)\;\frac{2}{3} \\ (d)\;0 \end {array}\]
Can you answer this question?

1 Answer

0 votes
$I= \int \limits_0^{\frac{\pi}{2}} \cos ^3 x dx$
$\quad= \int \limits_0^{\frac{\pi}{2}} \cos x (\cos ^2 x) dx$
$\quad= \int \limits_0^{\frac{\pi}{2}} \cos x (1-\sin ^2 x) dx$
$\quad= \int \limits_0^{\frac{\pi}{2}} \cos x dx -\int \limits_0^{\frac{\pi}{2}} \cos x \sin ^2 x dx$
$\sin x =t \quad \cos x dx=dt$
$\qquad= \sin x \bigg]_0^{\pi/2} - \int \limits _0^1 t^2 dt$
$\qquad=1-\large\frac{1}{3} $
Hence c is the correct answer.
answered Dec 21, 2013 by meena.p
Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App