What is the integral from 0 to 1/2 of sin(x^2) ?

The integral from 0 to 1/2 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi) 1/2)-sqrt(pi/2)\S(sqrt(2/pi)*0)

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integral from 0 to 1/2 of sin(x^2)

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

\frac{π}{2} § (\frac{2}{π} \frac{1}{2}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{\frac{1}{2}} 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}^{\frac{1}{2}}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \frac{1}{2}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} \frac{1}{2}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

What is the integral from 0 to 1/2 of sin(x^2) ?
The integral from 0 to 1/2 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi) 1/2)-sqrt(pi/2)\S(sqrt(2/pi)*0)