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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \limits_0^{\large\frac{z}{2}}$$ \cos x \sin ^3 x dx$

\[\begin {array} {1 1} (a)\;\frac{z}{2} \\ (b)\;\frac{z}{4} \\ (c)\;\frac{1}{4} \\ (d)\;\frac{1}{2} \end {array}\]

1 Answer

In that $m=3,n=1$ so formula will not apply directly,
$\sin x =t=> \cos x dx =dt$
at $x=0,t=0$
$x = \large\frac{z}{2}$$,t=1$
$\int \limits_0^1 t^3. dt$
$=\bigg[\large\frac{t^4}{4} \bigg]_0^1$
$=\bigg[\large\frac{1}{4}$$-0\bigg]$
$=\large\frac{1}{4}$

 

answered Dec 12, 2013 by meena.p
 
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