What is the integral from 0 to infinity of cos^2(x) ?

The integral from 0 to infinity of cos^2(x) is diverges

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integral from 0 to infinity of cos^2(x)

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

diverges

Solution steps

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

Compute the indefinite integral:

\int cos^{2} (x) d x = \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + C

Compute the boundaries:

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

diverges

= diverges

\int \frac{1}{64 e ^{- 8 x} + e ^{8 x}} d x

(5, 7), (- 4, - 2)

\int (e^{4 x} + e^{- 4 x})^{2} d x

f (x) = - \frac{10}{x ^{2}}

\int 8 - 2 x^{2} d x

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