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

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

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

\int_{0}^{π} cos (\frac{1}{2}) x d x

cos (\frac{1}{2}) \frac{π ^{2}}{2}

Decimal Notation

4.33069 \dots

Solution steps

\int_{0}^{π} cos (\frac{1}{2}) x d x

Take the constant out:

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

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

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{π}

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

Compute the boundaries:

\frac{π ^{2}}{2}

= cos (\frac{1}{2}) \frac{π ^{2}}{2}

x \to \frac{π}{2} lim (\frac{cos ( x )}{1 - sin ( x )})

x \to \frac{π}{2} lim (\frac{ln ( sin ( x ) )}{( π - 2 x ) ^{2}})

x \to 3 lim ((2 x - 4)^{4} (x - 2))

x \to 4 lim (\frac{x ^{2} + 4}{5})

x \to \frac{π}{2} lim (\frac{3 cos ^{2} ( x )}{2 - 2 sin ( x )})

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