What is the integral from 0 to pi of 4*sin(x) ?

The integral from 0 to pi of 4*sin(x) is 8

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integral from 0 to pi of 4*sin(x)

\int_{0}^{π} 4 \cdot sin (x) d x

8

Solution steps

\int_{0}^{π} 4 sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int_{0}^{π} sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= 4 [- cos (x)]_{0}^{π}

Compute the boundaries:

2

= 4 \cdot 2

Simplify

= 8

\int \frac{1}{( 1 + 2 x ) ^{2}} d x

\int 1 + e^{x^{2}} d x

\frac{\partial}{\partial y} (e^{x^{2} + y^{2}} \cdot 2 y)

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

\int_{0}^{2} 1 + 4 x^{2} d x

What is the integral from 0 to pi of 4*sin(x) ?
The integral from 0 to pi of 4*sin(x) is 8