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Popular >

integral from 0 to 2 of x^3(2-x)

Solution

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

Solution

\frac{8}{5}

+1

Decimal

1.6

Solution steps

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

Expand

x^{3} (2 - x) : 2 x^{3} - x^{4}

= \int_{0}^{2} 2 x^{3} - x^{4} 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}^{2} 2 x^{3} d x - \int_{0}^{2} x^{4} d x

\int_{0}^{2} 2 x^{3} d x = 8

\int_{0}^{2} x^{4} d x = \frac{32}{5}

= 8 - \frac{32}{5}

Simplify

8 - \frac{32}{5} : \frac{8}{5}

= \frac{8}{5}

Graph

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integral from 0 to y of (2x^2)/(y^2)

\int_{0}^{y} \frac{2 x ^{2}}{y ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x^3(2-x) ?
The integral from 0 to 2 of x^3(2-x) is 8/5