What is the integral from-1 to 1 of cos(x^2) ?

The integral from-1 to 1 of cos(x^2) is sqrt(pi/2)\C(sqrt(2/pi)*1)-sqrt(pi/2)\C(-1*sqrt(2/pi))

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integral from-1 to 1 of cos(x^2)

\int_{- 1}^{1} cos (x^{2}) d x

\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (- 1 \cdot \frac{2}{π})

Solution steps

\int_{- 1}^{1} 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)]_{- 1}^{1}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (- 1 \cdot \frac{2}{π})

= \frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (- 1 \cdot \frac{2}{π})

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What is the integral from-1 to 1 of cos(x^2) ?
The integral from-1 to 1 of cos(x^2) is sqrt(pi/2)\C(sqrt(2/pi)*1)-sqrt(pi/2)\C(-1*sqrt(2/pi))