What is the integral from 0 to pi of sqrt(cos^2(x)) ?

The integral from 0 to pi of sqrt(cos^2(x)) is 2

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integral from 0 to pi of sqrt(cos^2(x))

\int_{0}^{π} cos^{2} (x) d x

2

Solution steps

\int_{0}^{π} cos^{2} (x) d x

Apply exponent rule:

a^{2} = ∣ a ∣

= \int_{0}^{π} ∣ cos (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{π}{2}} cos (x) d x + \int_{\frac{π}{2}}^{π} - cos (x) d x

\int_{0}^{\frac{π}{2}} cos (x) d x = 1

\int_{\frac{π}{2}}^{π} - cos (x) d x = 1

= 1 + 1

Simplify

= 2

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What is the integral from 0 to pi of sqrt(cos^2(x)) ?
The integral from 0 to pi of sqrt(cos^2(x)) is 2