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

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

Popular >

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

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

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

Solution steps

\int_{0}^{x^{2}} 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}^{x^{2}}

Compute the boundaries:

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

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

\int_{- π}^{π} cos (\frac{x}{2}) d x

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

\int_{- \infty}^{0} e^{a x} d x

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

\int_{4}^{8} \frac{1}{x ^{2}} d x

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