( ^4 x - ^4 x ) ,dx = - Vidyadip

MCQ

$\int {\left( {{{\sin }^4}x - {{\cos }^4}x} \right)\,dx = } $

A
$ - \frac{{\cos 2x}}{2} + c$
✓
$ - \frac{{\sin 2x}}{2} + c$
C
$\frac{{\sin 2x}}{2} + c$
D
$\frac{{\cos 2x}}{2} + c$

✓

Answer

Correct option: B.

$ - \frac{{\sin 2x}}{2} + c$

b
(b)$\int {({{\sin }^4}x - {{\cos }^4}x)dx} = \int {({{\sin }^2}x - {{\cos }^2}x)} \,({\sin ^2}x + {\cos ^2}x)\,dx$
$ = \int {({{\sin }^2}x - {{\cos }^2}x)\,dx} $$ = - \int_{}^{} {({{\cos }^2}x - {{\sin }^2}x)dx} $
$ = - \int_{}^{} {\cos 2x\,dx} $$ = \frac{{ - \sin 2x}}{2} + c$.

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