What is the integral from-3 to 3 of sin(x^2) ?

The integral from-3 to 3 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*3)-sqrt(pi/2)\S(-3sqrt(2/pi))

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integral from-3 to 3 of sin(x^2)

\int_{- 3}^{3} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (- 3 \frac{2}{π})

Solution steps

\int_{- 3}^{3} 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)]_{- 3}^{3}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (- 3 \frac{2}{π})

= \frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (- 3 \frac{2}{π})

What is the integral from-3 to 3 of sin(x^2) ?
The integral from-3 to 3 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*3)-sqrt(pi/2)\S(-3sqrt(2/pi))