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

The integral from 0 to (3pi)/2 of 3|sin(x)| is 9

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

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

9

Solution steps

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

Eliminate Absolutes

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

\int_{0}^{π} 3 sin (x) d x = 6

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

= 6 + 3

Simplify

= 9

(y^{3} - t^{3}) d t - t y^{2} d y = 0, y (1) = 3

f (x) = \frac{5 - 4 x ^{2} + x ^{5}}{x ^{3}}

\frac{d y}{d x} = 8 x 25 - y^{2}

n = 1 \sum \infty 3 - \frac{2}{3 ^{n}}

\int_{b}^{2 b} x^{7} d x

What is the integral from 0 to (3pi)/2 of 3|sin(x)| ?
The integral from 0 to (3pi)/2 of 3|sin(x)| is 9