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

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

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integral from 0 to pi of cos(θ/2)

\int_{0}^{π} cos (\frac{θ}{2}) d θ

2

Solution steps

\int_{0}^{π} cos (\frac{θ}{2}) d θ

Apply u-substitution

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

Use the common integral:

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

= 2 [sin (u)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int_{- 2}^{2} 6 x d x

\int_{0}^{\frac{π}{4}} sin^{5} (2 y) d y

\int_{0}^{1} (x + 1) 1 - x d x

\int_{1}^{2} (- x^{2} + x + 2) d x

\int_{- 1}^{1} x 1 + x^{2} d x

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