2 pi 2 pi

Calculus Level 3

Evaluate

∫ − 2 π 2 π ∣ sin ⁡ x ∣ d x \int _{ -2\pi }^{ 2\pi }{ |\sin { x|dx } }

DETAILS

|y| is the modulus function.


The answer is 8.

Vighnesh Raut by Vighnesh Raut , 23, India

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1 solution

Tom Engelsman
Oct 4, 2020

This definite integral is identical to 4 ∫ 0 π sin ⁡ ( x ) d x = − 4 cos ⁡ ( x ) ∣ 0 π = 8 . 4\int_{0}^{\pi} \sin(x) dx = -4\cos(x)|_{0}^{\pi} = \boxed{8}.

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