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Popular Calculus >

integral from 2 to 0 of x^4-2x^3

Solution

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

Solution

\frac{8}{5}

+1

Decimal

1.6

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

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

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

= - (\frac{32}{5} - 8)

Simplify

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

= \frac{8}{5}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 2 to 0 of x^4-2x^3 ?
The integral from 2 to 0 of x^4-2x^3 is 8/5