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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \limits_0^{\frac{\pi}{2}} \sin^{\frac{3}{4}} \cos ^3 x dx$

\[\begin {array} {1 1} (a)\;\frac{4}{105} \\ (b)\;\frac{16}{105} \\ (c)\;\frac{32}{105} \\ (d)\;\frac{64}{105} \end {array}\]

Can you answer this question?
 
 

1 Answer

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$\int\limits_0^{\large\frac{\pi}{2}} \sin ^{3/4} \cos ^3 x dx$
$\sin x=t$
$\cos x dx=dt$
$\int \limits_0^1 t^{3/4} \large\frac{\cos ^3 x }{\cos x}$$dt$
$\qquad= \int \limits _0^1 t^{3/4} (1- \sin ^2 x) dt$
$\qquad= \int \limits _0^1 t^{3/4} (1- t^2 ) dt$
$\qquad= \large\frac{4}{7}-\frac{4}{15}$
$\qquad=\large\frac{32}{105}$
Hence c is the correct answer.

 

answered Dec 20, 2013 by meena.p
 
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