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

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

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integral from-pi to x^2 of sin(t^2)

\int_{- π}^{x^{2}} sin (t^{2}) d t

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

Solution steps

\int_{- π}^{x^{2}} sin (t^{2}) d t

Use the nonelementary integral:

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

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

Compute the boundaries:

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

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

\int_{0}^{3} t e^{- 0.3 t} d t

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\int_{2}^{5} \frac{1}{8 x + 9} d x

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