The value of $\int_{0}^{\pi}|\cos x|^{3} d x$ is:

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Definite Integrals

The value of

\int_{0}^{π} ∣ cos x ∣^{3} d x

is:

Answer: (B)

Because

∣ cos x ∣^{3}

is symmetric about

x = \frac{π}{2}

over

[0, π]

, the integral equals

2 \int_{0}^{π /2} cos^{3} x d x

. Using the reduction

\int_{0}^{π /2} cos^{3} x d x = \frac{2}{3}

, the value is

2 \times \frac{2}{3} = \frac{4}{3}

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

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