What is the integral from pi/2 to pi of 4cos(x) ?

The integral from pi/2 to pi of 4cos(x) is -4

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integral from pi/2 to pi of 4cos(x)

\int_{\frac{π}{2}}^{π} 4 cos (x) d x

- 4

Solution steps

\int_{\frac{π}{2}}^{π} 4 cos (x) d x

Take the constant out:

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

= 4 \cdot \int_{\frac{π}{2}}^{π} cos (x) d x

Use the common integral:

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

= 4 [sin (x)]_{\frac{π}{2}}^{π}

Compute the boundaries:

- 1

= 4 (- 1)

Simplify

= - 4

\int_{0}^{3} 3 x^{2} - 4 x + 1 d x

\int_{0}^{1} (x^{4} - x^{3}) d x

\int_{0}^{8} \frac{12}{x + 1} d x

\int_{21}^{x} \frac{1}{t} d t

\int_{π}^{0} sin^{4} (x) d x

What is the integral from pi/2 to pi of 4cos(x) ?
The integral from pi/2 to pi of 4cos(x) is -4