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Popular >

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

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Use the nonelementary integral:

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

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

Compute the boundaries:

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

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

Popular Examples

(\partial)/(\partial x)(x/(3+6x^2+7y^2))

\frac{\partial}{\partial x} (\frac{x}{3 + 6 x ^{2} + 7 y ^{2}})

derivative of 1/(x-1+1/(4-x))

\frac{d}{d x} (\frac{1}{x - 1} + \frac{1}{4 - x})

derivative of arcsin(xy)

\frac{d}{d x} (arcsin (x y))

f(x)=(xe^x)/(x+e^x)

f (x) = \frac{x e ^{x}}{x + e ^{x}}

integral of 4/((x+2)(x-2))

\int \frac{4}{( x + 2 ) ( x - 2 )} d x

Frequently Asked Questions (FAQ)

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