JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

f(x) = \left| \begin{array}{l} \sin \,\,x\,\, + \,\,\sin \,\,\,2x\,\, + \,\,\sin \,\,\,3x\,\,\,\sin \,\,\,2x\,\,\,\,\,\,\,\,\,\,\sin \,\,3x\\ \,\,\,\,\,3 + 4\sin x\;\,\,\,\,\,\,\,\,\,\;\;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4\,\,\sin \,\,x\\ 1\,\, + \,\,\sin \,\,x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\sin \,\,x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;1\;\;\;\; \end{array} \right|\,

, then the value of

\int \nolimits_0^{\pi /2} \,\,f\left( x \right)\,\,dx

View answer and explanation

Correct option: C

\frac{1}{3}

Option C (

\frac{1}{3}

) is correct because the determinant simplifies to

\sin 3x

, and the integral of

\sin 3x

from 0 to

\pi/2

\frac{1}{3}

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