What is the integral from 1 to 3 of sin(x^2) ?

The integral from 1 to 3 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*3)-sqrt(pi/2)\S(sqrt(2/pi)*1)

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integral from 1 to 3 of sin(x^2)

\int_{1}^{3} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

Solution steps

\int_{1}^{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)]_{1}^{3}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

= \frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (\frac{2}{π} \cdot 1)

\int_{a}^{b} 0 d x

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\int_{0}^{3} 1 + 4 r^{2} r d r

What is the integral from 1 to 3 of sin(x^2) ?
The integral from 1 to 3 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*3)-sqrt(pi/2)\S(sqrt(2/pi)*1)