What is the integral from 0 to infinity of cos(pix) ?

The integral from 0 to infinity of cos(pix) is diverges

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integral from 0 to infinity of cos(pix)

\int_{0}^{\infty} cos (π x) d x

diverges

Solution steps

\int_{0}^{\infty} cos (π x) d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} cos (π x) d x =

diverges

= diverges

\int 8 cos^{2} (x) d x

(1 x y^{2} + 4 y) d x + (1 x^{2} y + 4 x) d y = 0

y = x^{2} - 6 x + 9

\frac{d}{d x} (a x^{2} + b x)

\int_{1}^{2} (\frac{1}{8} + \frac{3}{8} x) d x

What is the integral from 0 to infinity of cos(pix) ?
The integral from 0 to infinity of cos(pix) is diverges