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

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

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integral from 0 to pi/2 of cos(2u)

\int_{0}^{\frac{π}{2}} cos (2 u) d u

0

Solution steps

\int_{0}^{\frac{π}{2}} cos (2 u) d u

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} [sin (v)]_{0}^{π}

Compute the boundaries:

0

= \frac{1}{2} \cdot 0

Simplify

= 0

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