What is the integral from 0 to infinity of sin^2(α) ?

The integral from 0 to infinity of sin^2(α) is diverges

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integral from 0 to infinity of sin^2(α)

\int_{0}^{\infty} sin^{2} (α) d α

diverges

Solution steps

\int_{0}^{\infty} sin^{2} (α) d α

Compute the indefinite integral:

\int sin^{2} (α) d α = \frac{1}{2} (α - \frac{1}{2} sin (2 α)) + C

Compute the boundaries:

\int_{0}^{\infty} sin^{2} (α) d α =

diverges

= diverges

\int_{- 1}^{2} ∣ x - 1 ∣ sin (x) d x

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

\int_{0}^{- 1} x^{3} 1 - x^{2} d x

\int_{0}^{1} 2 x arccos (x) d x

\int_{0}^{2} 3 x + 1 d x

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