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 (2x-x^3)

Solution

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

Solution

\frac{45}{4}

+1

Decimal

11.25

Solution steps

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

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

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

\int_{0}^{3} 2 x d x = 9

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

= - (9 - \frac{81}{4})

Simplify

- (9 - \frac{81}{4}) : \frac{45}{4}

= \frac{45}{4}

Graph

Popular Examples

integral from 0 to 10 of 1/((1+x)^2)

\int_{0}^{10} \frac{1}{( 1 + x ) ^{2}} d x

integral from 1 to 6 of |4x-8|

\int_{1}^{6} ∣ 4 x - 8 ∣ d x

integral from 0 to a of sin((npix)/a)

\int_{0}^{a} sin (\frac{nπ x}{a}) d x

integral from 1 to 7 of (1/x)

\int_{1}^{7} (\frac{1}{x}) d x

integral from 0 to infinity of sin(2t)

\int_{0}^{\infty} sin (2 t) d t

Frequently Asked Questions (FAQ)

What is the integral from 3 to 0 of (2x-x^3) ?
The integral from 3 to 0 of (2x-x^3) is 45/4