What is the integral from 0 to y/2 of cos(y^2) ?

The integral from 0 to y/2 of cos(y^2) is sqrt(pi/2)\C(sqrt(2/pi) y/2)-sqrt(pi/2)\C(sqrt(2/pi)*0)

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integral from 0 to y/2 of cos(y^2)

\int_{0}^{\frac{y}{2}} cos (y^{2}) d y

\frac{π}{2} C (\frac{2}{π} \frac{y}{2}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{\frac{y}{2}} cos (y^{2}) d y

Use the nonelementary integral:

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

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

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} \frac{y}{2}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

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

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