What is the integral from 0 to x^3 of cos(t^2) ?

The integral from 0 to x^3 of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)x^3)-sqrt(pi/2)\C(sqrt(2/pi)*0)

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integral from 0 to x^3 of cos(t^2)

\int_{0}^{x^{3}} cos (t^{2}) d t

\frac{π}{2} C (\frac{2}{π} x^{3}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

Solution steps

\int_{0}^{x^{3}} cos (t^{2}) d t

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} t)]_{0}^{x^{3}}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} x^{3}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= \frac{π}{2} C (\frac{2}{π} x^{3}) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

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What is the integral from 0 to x^3 of cos(t^2) ?
The integral from 0 to x^3 of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)x^3)-sqrt(pi/2)\C(sqrt(2/pi)*0)