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

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

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

\int_{0}^{\infty} sin (\frac{x}{2}) d x

diverges

Solution steps

\int_{0}^{\infty} sin (\frac{x}{2}) d x

Compute the indefinite integral:

\int sin (\frac{x}{2}) d x = - 2 cos (\frac{x}{2}) + C

Compute the boundaries:

\int_{0}^{\infty} sin (\frac{x}{2}) d x =

diverges

= diverges

\int_{0}^{π} sin (x) + cos (x) d x

\int_{0}^{1} e^{- s t} (2 t + 1) d t

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

\int_{- 1}^{1} cosh (x) d x

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

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