What is the integral from x^4 to 0 of cos(t^2) ?

The integral from x^4 to 0 of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)*0)-sqrt(pi/2)\C(sqrt(2/pi)x^4)

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integral from x^4 to 0 of cos(t^2)

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

\frac{π}{2} C (\frac{2}{π} \cdot 0) - \frac{π}{2} C (\frac{2}{π} x^{4})

Solution steps

\int_{x^{4}}^{0} 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)]_{x^{4}}^{0}

Compute the boundaries:

\frac{π}{2} C (\frac{2}{π} \cdot 0) - \frac{π}{2} C (\frac{2}{π} x^{4})

= \frac{π}{2} C (\frac{2}{π} \cdot 0) - \frac{π}{2} C (\frac{2}{π} x^{4})

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

\int_{5}^{\infty} \frac{1}{x} d x

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

\int_{0}^{1} x (1 - x)^{3} d x

\int_{0}^{4} \frac{1}{x - 2} d x

What is the integral from x^4 to 0 of cos(t^2) ?
The integral from x^4 to 0 of cos(t^2) is sqrt(pi/2)\C(sqrt(2/pi)*0)-sqrt(pi/2)\C(sqrt(2/pi)x^4)