What is the integral from 0 to 1 of 12cos(x^2) ?

The integral from 0 to 1 of 12cos(x^2) is 12(sqrt(pi/2)\C(sqrt(2/pi)*1)-sqrt(pi/2)\C(sqrt(2/pi)*0))

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integral from 0 to 1 of 12cos(x^2)

\int_{0}^{1} 12 cos (x^{2}) d x

12 (\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0))

Solution steps

\int_{0}^{1} 12 cos (x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 12 \cdot \int_{0}^{1} cos (x^{2}) d x

Use the nonelementary integral:

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

= 12 [\frac{π}{2} C (\frac{2}{π} x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= 12 (\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0))

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What is the integral from 0 to 1 of 12cos(x^2) ?
The integral from 0 to 1 of 12cos(x^2) is 12(sqrt(pi/2)\C(sqrt(2/pi)*1)-sqrt(pi/2)\C(sqrt(2/pi)*0))