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

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

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integral from 0 to x^2 of sin(θ^2)

\int_{0}^{x^{2}} sin (θ^{2}) d θ

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

Solution steps

\int_{0}^{x^{2}} sin (θ^{2}) d θ

Use the nonelementary integral:

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

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

Compute the boundaries:

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

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

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