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Popular >

integral from 0 to 3 of x(1+x^2)

Solution

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

Solution

\frac{99}{4}

+1

Decimal

24.75

Solution steps

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

Expand

x (1 + x^{2}) : x + x^{3}

= \int_{0}^{3} x + x^{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{3} x d x + \int_{0}^{3} x^{3} d x

\int_{0}^{3} x d x = \frac{9}{2}

\int_{0}^{3} x^{3} d x = \frac{81}{4}

= \frac{9}{2} + \frac{81}{4}

Simplify

\frac{9}{2} + \frac{81}{4} : \frac{99}{4}

= \frac{99}{4}

Graph

Popular Examples

integral from 9 to 36 of 1/(sqrt(x))

\int_{9}^{36} \frac{1}{x} d x

integral from sqrt(3) to 3 of 8/(9+x^2)

\int_{3}^{3} \frac{8}{9 + x ^{2}} d x

integral from 0 to 1 of 1/2 x+1/2-x^2

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

integral from 0 to 3 of 1/((x-1))

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

integral from 0 to 5 of 2.5x

\int_{0}^{5} 2.5 x d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of x(1+x^2) ?
The integral from 0 to 3 of x(1+x^2) is 99/4