What is the integral from 0 to (3pi)/4 of |cos(x)| ?

The integral from 0 to (3pi)/4 of |cos(x)| is -1/(sqrt(2))+2

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integral from 0 to (3pi)/4 of |cos(x)|

\int_{0}^{\frac{3 π}{4}} ∣ cos (x) ∣ d x

- \frac{1}{2} + 2

Decimal

1.29289 \dots

Solution steps

\int_{0}^{\frac{3 π}{4}} ∣ cos (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{\frac{π}{2}} cos (x) d x + \int_{\frac{π}{2}}^{\frac{3 π}{4}} - cos (x) d x

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

\int_{\frac{π}{2}}^{\frac{3 π}{4}} - cos (x) d x = - \frac{1}{2} + 1

= 1 - \frac{1}{2} + 1

Simplify

= - \frac{1}{2} + 2

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What is the integral from 0 to (3pi)/4 of |cos(x)| ?
The integral from 0 to (3pi)/4 of |cos(x)| is -1/(sqrt(2))+2