What is the integral from 0 to x of cos(t^2) ?

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

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integral from 0 to x of cos(t^2)

\int_{0}^{x} cos (t^{2}) d t

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

Solution steps

\int_{0}^{x} cos (t^{2}) d t

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} t)]_{0}^{x}

Compute the boundaries:

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

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

\int_{0}^{\frac{π}{3}} cos (x) d x

\int_{\frac{π}{3}}^{π} sin (x + \frac{π}{3}) d x

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

\int_{0}^{4} 6 x^{3} - 3 x d x

\int_{- 2}^{3} \frac{1}{x + 3} d x

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