The value of $\mathop \smallint \limits_a^{a + \left( {\pi /2} \right)} \,\,\left( {{{\sin }^4}\,\,x\,\, + \,\,{{\cos }^4}\,\,x} \right)\,\,dx$, is

$a\,\,{\left( {\frac{\pi }{2}} \right)^2}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \limits_a^{a + \left( {\pi /2} \right)} \,\,\left( {{{\sin }^4}\,\,x\,\, + \,\,{{\cos }^4}\,\,x} \right)\,\,dx

, is

View answer and explanation

Correct option: A

\frac{{3\,\pi }}{8}

Option A is correct because the integral of a periodic function over one period is independent of the starting point, and the integral is evaluated to be 3π/8.

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