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

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

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

\int_{0}^{2 π} cos (\frac{x}{2}) d x

0

Solution steps

\int_{0}^{2 π} cos (\frac{x}{2}) d x

Apply u-substitution

= \int_{0}^{π} cos (u) \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int_{0}^{π} cos (u) d u

Use the common integral:

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

= 2 [sin (u)]_{0}^{π}

Compute the boundaries:

0

= 2 \cdot 0

Simplify

= 0

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