Integrals (3)

Calculus Level 2

Evaluate ∫ 0 2 π ∣ cos ⁡ x ∣ d x . \int_0^{2\pi } |\cos x | \, dx .


Notation: ∣ ⋅ ∣ | \cdot | denotes the absolute value function .


The answer is 4.

Aman Sharma by Aman Sharma , 25, India

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1 solution

Christian Zinck
Dec 15, 2014

The graph of absolute value of cos(x) from 0 to 2(pi) is 4 half periods of cos(x). Therefore one can find the integral from 0 to pi/2 of cos(x)dx times 4 to calculate the the integral from 0 to 2(pi) of the absolute value of cos(x)dx. By doing that, the answer 4 is achieved.

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