The value of $\mathop \smallint \nolimits_0^{\rm{\pi }} \,\,|{\sin ^3}\,\,{\rm{\theta }}|\,\,d{\rm{\theta }}$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \nolimits_0^\mathrm{\pi } \,\,|{\sin ^3}\,\,\mathrm{\theta }|\,\,d\mathrm{\theta }

View answer and explanation

Correct option: C

\mathrm{4}\,\mathrm{/}\,\mathrm{3}

Option C (

\frac{4}{3}

) is correct because the integral of |sin³θ| from 0 to π is equal to the integral of sin³θ from 0 to π, which evaluates to 4/3.

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