The value of the integral $\mathop \smallint \limits_0^{\pi /2} \,\,\left| {\,\sin \,\,x\,\, - \,\,\cos \,\,x\,} \right|\,\,dx$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int \limits_0^{\pi /2} \,\,\left| {\,\sin \,\,x\,\, - \,\,\cos \,\,x\,} \right|\,\,dx

, is

View answer and explanation

Correct option: B

2\,\,\left( {\sqrt 2 - 1} \right)

Option B (

2\,\,\left( {\sqrt 2 - 1} \right)

) is correct because the integral of the absolute value function splits into two integrals, and the result is

2\sqrt{2} - 2

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