If $\smallint \,\,{\cos ^4}\,x\,\,dx = Ax\,\, + \,\,B\,\,\sin \,\,2\,x\,\, + \,\,C\,\,\sin \,\,4x\,\, + \,\,D$ , then {A,B,C} equals

$\left\{ {\frac{3}{8},\,\,\frac{1}{{32}}\,\,,\,\,\frac{1}{4}} \right\}$

$\left\{ {\frac{1}{{32}},\,\,\frac{1}{4},\,\,\frac{3}{8}} \right\}$

$\left\{ {\frac{1}{4},\,\,\frac{3}{8},\,\,\frac{1}{{32}}} \right\}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium

1 of 1

Application +4 | -1

\int \,\,{\cos ^4}\,x\,\,dx = Ax\,\, + \,\,B\,\,\sin \,\,2\,x\,\, + \,\,C\,\,\sin \,\,4x\,\, + \,\,D

, then {A,B,C} equals

View answer and explanation

Correct option: B

\left\{ {\frac{3}{8},\,\,\frac{1}{4},\,\,\frac{1}{{32}}} \right\}

Option B (

\left\{{{\frac{3}{8},\\,\frac{1}{4},\\,\frac{1}{{32}}}}\right\}

) is correct because the integral of

\cos^4 x

is evaluated using trigonometric identities and then the coefficients are matched.