What is the integral from 0 to 3 of sin(x^2) ?

The integral from 0 to 3 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*3)-sqrt(pi/2)\S(sqrt(2/pi)*0)

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integral from 0 to 3 of sin(x^2)

\int_{0}^{3} sin (x^{2}) d x

\frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{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)]_{0}^{3}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} \cdot 3) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

\frac{d y}{d x} = y^{2} + y

y = arccos (x)

x \to π lim (sin (\frac{5}{3} x))

\frac{\partial}{\partial y} (x yz + x y^{4} + y z^{4} + z x^{4})

\frac{3}{s ^{2} + 2 s + 1}

What is the integral from 0 to 3 of sin(x^2) ?
The integral from 0 to 3 of sin(x^2) is sqrt(pi/2)\S(sqrt(2/pi)*3)-sqrt(pi/2)\S(sqrt(2/pi)*0)