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

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

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

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

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{0}^{\frac{π}{2}} 1 d x = \frac{π}{2}

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

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

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