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

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

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integral from y to 1 of sin(x^2)

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

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

Solution steps

\int_{y}^{1} 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)]_{y}^{1}

Compute the boundaries:

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

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

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