What is the integral from 0 to (3pi)/2 of 6|sin(x)| ?

The integral from 0 to (3pi)/2 of 6|sin(x)| is 18

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integral from 0 to (3pi)/2 of 6|sin(x)|

\int_{0}^{\frac{3 π}{2}} 6 ∣ sin (x) ∣ d x

18

Solution steps

\int_{0}^{\frac{3 π}{2}} 6 ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{π} 6 sin (x) d x + \int_{π}^{\frac{3 π}{2}} 6 (- sin (x)) d x

\int_{0}^{π} 6 sin (x) d x = 12

\int_{π}^{\frac{3 π}{2}} 6 (- sin (x)) d x = 6

= 12 + 6

Simplify

= 18

\int cos^{7} (\frac{1}{3}) x d x

\int 12 x^{2} - 6 x d x

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

\int 1 + \frac{1}{x ^{\frac{2}{3}}} d x

x \to 1 lim (5 x^{2} + 1)

What is the integral from 0 to (3pi)/2 of 6|sin(x)| ?
The integral from 0 to (3pi)/2 of 6|sin(x)| is 18