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

Integrate :$\int \limits_0^{\frac{\pi}{4}}$$ \large\frac{\sin ^3 x}{\cos ^7 x}$$dx$

\[\begin {array} {1 1} (a)\;\frac{1}{6} \\ (b)\;\frac{1}{4} \\ (c)\;\frac{7}{12} \\ (d)\;\frac{5}{12} \end {array}\]

1 Answer

$\tan x=t$
$\sec^2 x dx= dt$
$\int \limits_0^{\frac{\pi}{4}} \large\frac{\tan^3 x}{\cos ^4 x}$$dx=\int \limits_0^1 \large\frac{t^3 \sec^4 }{\sec^2 x}$$ dt $
$\qquad= \int \limits_0^1 t^3 (1+t^2) dt$
$\qquad= \large\frac{t^4}{4}+\frac{t^6}{6} \bigg]_0^1$
$\qquad=\large\frac{5}{12}$
Hence d is the correct answer
answered Dec 20, 2013 by meena.p
 
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