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Popular >

integral from 0 to x of x^2sin(t^2)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= x^{2} \cdot \int_{0}^{x} sin (t^{2}) d t

Use the nonelementary integral:

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

= x^{2} [\frac{π}{2} § (\frac{2}{π} t)]_{0}^{x}

Compute the boundaries:

\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

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

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Frequently Asked Questions (FAQ)

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