What is the integral from-pi/2 to pi/2 of xcos(x^2) ?

The integral from-pi/2 to pi/2 of xcos(x^2) is 0

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integral from-pi/2 to pi/2 of xcos(x^2)

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

0

Solution steps

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

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

x cos (x^{2}) :

Odd

= 0

\int_{1}^{7} \frac{x}{7} - \frac{7}{x} d x

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\int_{x}^{x} sin (t^{2} - 1) d t

\int_{2}^{4} - x + 4 d x

\int_{1}^{e} x^{9} ln (x) d x

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