The value of the definite integral $\mathop \smallint \nolimits_{a + 2\pi }^{a + 5\pi /2} \,\,({\sin ^{ - 1}}\,\,(\cos \,\,x) + {\cos ^{ - 1}}\,\,(\sin \,x))\;dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the definite integral

\int \nolimits_{a + 2\pi }^{a + 5\pi /2} \,\,({\sin ^{ - 1}}\,\,(\cos \,\,x) + {\cos ^{ - 1}}\,\,(\sin \,x))\;dx

is equal to

View answer and explanation

Correct option: B

\frac{{{\mathrm{\pi }^2}}}{4}

Option B (

\frac{{{\mathrm{\pi }^2}}}{4}

) is correct because after simplifying the integrand using inverse trigonometric identities and evaluating the integral, the result is this value.

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