What is the integral from 2x to 10 of cos(y^2) ?

The integral from 2x to 10 of cos(y^2) is sqrt(pi/2)\C(sqrt(2/pi)*10)-sqrt(pi/2)\C(sqrt(2/pi)*2x)

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integral from 2x to 10 of cos(y^2)

\int_{2 x}^{10} cos (y^{2}) d y

\frac{π}{2} C (\frac{2}{π} \cdot 10) - \frac{π}{2} C (\frac{2}{π} \cdot 2 x)

Solution steps

\int_{2 x}^{10} cos (y^{2}) d y

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} y)]_{2 x}^{10}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} \cdot 10) - \frac{π}{2} C (\frac{2}{π} \cdot 2 x)

= \frac{π}{2} C (\frac{2}{π} \cdot 10) - \frac{π}{2} C (\frac{2}{π} \cdot 2 x)

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos^{2} (u) d u

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

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

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

\int_{0}^{5} 4 - x^{2} d x

What is the integral from 2x to 10 of cos(y^2) ?
The integral from 2x to 10 of cos(y^2) is sqrt(pi/2)\C(sqrt(2/pi)*10)-sqrt(pi/2)\C(sqrt(2/pi)*2x)