The value of $\mathop \smallint \limits_0^2 \,\,\left| {\cos \,\,\left( {\frac{{\pi x}}{2}} \right)\,} \right|$, is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \limits_0^2 \,\,\left| {\cos \,\,\left( {\frac{{\pi x}}{2}} \right)\,} \right|

, is

View answer and explanation

Correct option: D

4/\pi

Option D (4/π) is correct because the integral of |cos(πx/2)| from 0 to 2 is calculated by splitting the integral at x=1 where cos(πx/2) changes sign.

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