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

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

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

\int_{0}^{π} sin (\frac{x}{2}) d x

2

Solution steps

\int_{0}^{π} sin (\frac{x}{2}) d x

Apply u-substitution

: \int_{0}^{\frac{π}{2}} sin (u) \cdot 2 d u

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

Use the common integral:

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

= 2 [- cos (u)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int \frac{1 + x ^{2} + 1}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\int 17 x e^{- x^{2}} d x

\frac{d y}{d x} = \frac{cos ( 13 x )}{e ^{13 y}}

\int 7^{- 2 x} d x

\frac{d}{d x} (5 x - 2)

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