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

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

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

\int_{0}^{2 π} cos (x^{2}) d x

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

Solution steps

\int_{0}^{2 π} 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}^{2 π}

Compute the boundaries:

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

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

\int_{0}^{4} 4 - x^{2} - (4 - 4 x) d x

\int_{1}^{4} - 2 x + 6 d x

\int_{- 1}^{2} \frac{1}{x ^{2} - 4 x + 13} d x

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

\int_{1}^{2} π (4 - \frac{1}{2} x)^{2} d x

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