What is the integral of sin(θ^2) ?

The integral of sin(θ^2) is sqrt(pi/2)\S(sqrt(2/pi)θ)+C

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integral of sin(θ^2)

\int sin (θ^{2}) d θ

\frac{π}{2} § (\frac{2}{π} θ) + C

Solution steps

\int 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)

Add a constant to the solution

= \frac{π}{2} § (\frac{2}{π} θ) + C

What is the integral of sin(θ^2) ?
The integral of sin(θ^2) is sqrt(pi/2)\S(sqrt(2/pi)θ)+C