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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate: $\int \limits_0^{z/4} \sin ^4 (2x)dx $

\[\begin {array} {1 1} (a)\;\frac{z}{16} \\ (b)\;\frac{3z}{32} \\ (c)\;\frac{5z}{16} \\ (d)\;\frac{3z}{16} \end {array}\]

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1 Answer

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$2x=t=>2dx=2dt$
at $x=0,t=0, x=\large\frac{z}{4}$$,t= \large\frac{z}{2}$
=> $\large\frac{1}{2} \int _0^{z/2} $$ \sin ^4 (t) dt$
=> $n=4, $ even. $k= \large\frac{z}{2}$
=> By for, $\large\frac{1}{2} \times \frac{(4-1)(4-3)}{4(4-2)}. \frac{\pi}{2}$
=> $\large\frac{1}{2} \times \frac{3.1}{4.2} .\frac{z}{2}$
=> $\large\frac{3z}{32}$
Hence b is the correct answer.
answered Dec 12, 2013 by meena.p
 
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