What is the integral from 0 to (3pi)/2 of |cos(x)| ?

The integral from 0 to (3pi)/2 of |cos(x)| is 3

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integral from 0 to (3pi)/2 of |cos(x)|

\int_{0}^{\frac{3 π}{2}} ∣ cos (x) ∣ d x

3

Solution steps

\int_{0}^{\frac{3 π}{2}} ∣ cos (x) ∣ d x

Eliminate Absolutes

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

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

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

= 1 + 2

Simplify

= 3

d er i v a t i v e f (x) = \frac{2}{2 x + 1}

d er i v a t i v e \frac{2 z ^{3}}{3} - z

y y^{^{'}} - 21 e^{x} = 0

d er i v a t i v e (1 - t) (1 + t^{2})^{- 1}

\frac{\partial}{\partial y} (ln (x - 9 y))

What is the integral from 0 to (3pi)/2 of |cos(x)| ?
The integral from 0 to (3pi)/2 of |cos(x)| is 3