What is the integral from 0 to (3pi)/2 of 5|sin(x)| ?

The integral from 0 to (3pi)/2 of 5|sin(x)| is 15

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integral from 0 to (3pi)/2 of 5|sin(x)|

\int_{0}^{\frac{3 π}{2}} 5 ∣ sin (x) ∣ d x

15

Solution steps

\int_{0}^{\frac{3 π}{2}} 5 ∣ sin (x) ∣ d x

Eliminate Absolutes

= \int_{0}^{π} 5 sin (x) d x + \int_{π}^{\frac{3 π}{2}} 5 (- sin (x)) d x

\int_{0}^{π} 5 sin (x) d x = 10

\int_{π}^{\frac{3 π}{2}} 5 (- sin (x)) d x = 5

= 10 + 5

Simplify

= 15

\frac{x ^{2}}{2 + x}

\int_{- 1}^{64} \frac{1}{x ^{\frac{1}{3}}} d x

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

x \to 2 lim (3 + 2 x + x^{2})

x \to 3 lim (\frac{∣ x - 3 ∣}{x + 3})

What is the integral from 0 to (3pi)/2 of 5|sin(x)| ?
The integral from 0 to (3pi)/2 of 5|sin(x)| is 15