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Popular >

integral from 3 to 0 of 5x-x^3

Solution

\int_{3}^{0} 5 x - x^{3} d x

Solution

- \frac{9}{4}

+1

Decimal Notation

- 2.25

Solution steps

\int_{3}^{0} 5 x - x^{3} d x

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

= - \int_{0}^{3} 5 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} 5 x d x - \int_{0}^{3} x^{3} d x)

\int_{0}^{3} 5 x d x = \frac{45}{2}

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

= - (\frac{45}{2} - \frac{81}{4})

Join

\frac{45}{2} - \frac{81}{4} : \frac{9}{4}

= - \frac{9}{4}

Popular Examples

integral from 3 to 7 of x/(x-7)

\int_{3}^{7} \frac{x}{x - 7} d x

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

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

integral from 0 to 1 of 12x(1-x)^2

\int_{0}^{1} 12 x (1 - x)^{2} d x

integral from 0 to 1 of 4xe^{7x}

\int_{0}^{1} 4 x e^{7 x} d x

integral from 1 to e of (8ln(x))

\int_{1}^{e} (8 ln (x)) d x

Frequently Asked Questions (FAQ)

What is the integral from 3 to 0 of 5x-x^3 ?
The integral from 3 to 0 of 5x-x^3 is -9/4