The value of the integral $\int_{0}^{\pi}|\sin 2 x| d x$ is ______.

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Definite Integrals

The value of the integral

\int_{0}^{π} ∣ sin 2 x ∣ d x

is ______.

Answer: 2

[0, \frac{π}{2}]

the function

sin 2 x

is non-negative and on

[\frac{π}{2}, π]

it is non-positive, so

\int_{0}^{π} ∣ sin 2 x ∣ d x = \int_{0}^{π /2} sin 2 x d x - \int_{π /2}^{π} sin 2 x d x

= [- \frac{cos 2 x}{2}]_{0}^{π /2} + [\frac{cos 2 x}{2}]_{π /2}^{π} = 1 + 1 = 2

The value of the integral is

2

JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Integer answer

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