The value of the integral $\mathop \smallint \limits_{ - \pi }^\pi {\left( {\cos \,\,ax\,\, - \,\,\sin \,\,bx} \right)^2}dx$, where ($a$ and $b$ integers), is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int \limits_{ - \pi }^\pi {\left( {\cos \,\,ax\,\, - \,\,\sin \,\,bx} \right)^2}dx

, where (

a

and

b

integers), is

View answer and explanation

Correct option: D

2\,\pi

Option D (

2\,\pi

) is correct because it involves integrating trigonometric functions over a symmetric interval, utilizing their properties.

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