What is the integral from 0 to pi/4 of cos(x^2) ?

The integral from 0 to pi/4 of cos(x^2) is sqrt(pi/2)\C(sqrt(2/pi) pi/4)-sqrt(pi/2)\C(sqrt(2/pi)*0)

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integral from 0 to pi/4 of cos(x^2)

\int_{0}^{\frac{π}{4}} cos (x^{2}) d x

\frac{π}{2} C (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{\frac{π}{4}} cos (x^{2}) d x

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} x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= \frac{π}{2} C (\frac{2}{π} \frac{π}{4}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

\int_{- 1}^{5} 1 + 3 x d x

\int_{1}^{5} \frac{1}{x - 6} d x

\int_{- 2}^{x} (26 t^{2} - 25 t) d t

\int_{0}^{t} e^{- 2 t} d t

\int_{- 1}^{0} x e^{- x} d x

What is the integral from 0 to pi/4 of cos(x^2) ?
The integral from 0 to pi/4 of cos(x^2) is sqrt(pi/2)\C(sqrt(2/pi) pi/4)-sqrt(pi/2)\C(sqrt(2/pi)*0)