What is the integral from 0 to pi/2 of 1/2 cos(x) ?

The integral from 0 to pi/2 of 1/2 cos(x) is 1/2

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integral from 0 to pi/2 of 1/2 cos(x)

\int_{0}^{\frac{π}{2}} \frac{1}{2} cos (x) d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{0}^{\frac{π}{2}} \frac{1}{2} cos (x) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{\frac{π}{2}} cos (x) d x

Use the common integral:

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

= \frac{1}{2} [sin (x)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= \frac{1}{2} \cdot 1

Simplify

= \frac{1}{2}

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What is the integral from 0 to pi/2 of 1/2 cos(x) ?
The integral from 0 to pi/2 of 1/2 cos(x) is 1/2