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

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

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

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

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

Solution steps

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

Use the nonelementary integral:

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

= [\frac{π}{2} § (\frac{2}{π} y)]_{0}^{x}

Compute the boundaries:

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

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

\int_{- 2}^{x} 1 - x^{4} d x

\int_{2}^{3} \frac{x}{ln ( x - 1 )} d x

\int_{- 2}^{3} \frac{2}{x ^{3}} d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} u cos (u) d u

\int_{- 2}^{1} (2 x + 2) d x

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