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

The integral from x to x^3 of sin(t^2) is sqrt(pi/2)\S(sqrt(2/pi)x^3)-sqrt(pi/2)\S(sqrt(2/pi)x)

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integral from x to x^3 of sin(t^2)

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

\frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} x)

Solution steps

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

Use the nonelementary integral:

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= [\frac{π}{2} § (\frac{2}{π} t)]_{x}^{x^{3}}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} x)

= \frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} x)

\int_{0}^{2} (6 x - 3) (4 x^{2} + 5) d x

\int_{- \frac{π}{2}}^{\frac{π}{2}} cos (x) - 3 d x

\int_{0}^{\frac{1}{2}} 3 x^{2} d x

\int_{0}^{2} x^{2} 1 + 4 x^{2} d x

\int_{0}^{1} (2 - 2 x^{3})^{3} d x

What is the integral from x to x^3 of sin(t^2) ?
The integral from x to x^3 of sin(t^2) is sqrt(pi/2)\S(sqrt(2/pi)x^3)-sqrt(pi/2)\S(sqrt(2/pi)x)