en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

y^'=(3y^2+3)/(2xy)

y^{^{'}} = \frac{3 y ^{2} + 3}{2 x y}

(dy)/(dx)=6sqrt(xy)

\frac{d y}{d x} = 6 x y

integral of sqrt((x^2+1)/(x^2))

\int \frac{x ^{2} + 1}{x ^{2}} d x

(dy)/(dx)=10^{x+y}

\frac{d y}{d x} = 1 0^{x + y}

derivative of x(s-2x(s-2x))

\frac{d}{d x} (x (s - 2 x) (s - 2 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