What is the integral from 0 to 2pi of sin(x^2) ?

The integral from 0 to 2pi of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*2pi)-sqrt(pi/2)\S(sqrt(2/pi)*0)

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integral from 0 to 2pi of sin(x^2)

\int_{0}^{2 π} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} \cdot 2 π) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{2 π} sin (x^{2}) d x

Use the nonelementary integral:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= [\frac{π}{2} § (\frac{2}{π} x)]_{0}^{2 π}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \cdot 2 π) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} \cdot 2 π) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

\int_{- x}^{x} 3 + 4 t^{2} d t

\int_{0}^{1} sinh (x) d x

\int_{\frac{1}{x}}^{4} 1 + \frac{1}{t} d t

\int_{2}^{4} e^{- s t} t^{2} d t

\int_{0}^{4} 2^{x^{2}} d x

What is the integral from 0 to 2pi of sin(x^2) ?
The integral from 0 to 2pi of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*2pi)-sqrt(pi/2)\S(sqrt(2/pi)*0)