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

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

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integral from 0 to 2 of sin(-x^2)

\int_{0}^{2} sin (- x^{2}) d x

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

Solution steps

\int_{0}^{2} sin (- x^{2}) d x

Simplify

sin (- x^{2}) : - sin (x^{2})

= \int_{0}^{2} - sin (x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int_{0}^{2} 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)]_{0}^{2}

Compute the boundaries:

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

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

Simplify

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

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