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Popular Calculus >

integral from 3 to 0 of (4x-x^3)

Solution

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

Solution

\frac{9}{4}

+1

Decimal

2.25

Solution steps

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

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

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

\int_{0}^{3} 4 x d x = 18

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

= - (18 - \frac{81}{4})

Simplify

- (18 - \frac{81}{4}) : \frac{9}{4}

= \frac{9}{4}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 3 to 0 of (4x-x^3) ?
The integral from 3 to 0 of (4x-x^3) is 9/4