What is the integral from-pi/2 to pi of 5cos(x) ?

The integral from-pi/2 to pi of 5cos(x) is 5

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integral from-pi/2 to pi of 5cos(x)

\int_{- \frac{π}{2}}^{π} 5 cos (x) d x

5

Solution steps

\int_{- \frac{π}{2}}^{π} 5 cos (x) d x

Take the constant out:

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

= 5 \cdot \int_{- \frac{π}{2}}^{π} cos (x) d x

Use the common integral:

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

= 5 [sin (x)]_{- \frac{π}{2}}^{π}

Compute the boundaries:

1

= 5 \cdot 1

Simplify

= 5

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What is the integral from-pi/2 to pi of 5cos(x) ?
The integral from-pi/2 to pi of 5cos(x) is 5