en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 3 of x(x-7)

Solution

\int_{0}^{3} x (x - 7) d x

Solution

- \frac{45}{2}

+1

Decimal

- 22.5

Solution steps

\int_{0}^{3} x (x - 7) d x

Expand

x (x - 7) : x^{2} - 7 x

= \int_{0}^{3} x^{2} - 7 x 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} x^{2} d x - \int_{0}^{3} 7 x d x

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

\int_{0}^{3} 7 x d x = \frac{63}{2}

= 9 - \frac{63}{2}

Simplify

9 - \frac{63}{2} : - \frac{45}{2}

= - \frac{45}{2}

Graph

Popular Examples

integral from 1 to 2 of 1 (sqrt(3+5t^4))

\int_{1}^{2} \frac{d}{1} (3 + 5 t^{4}) d x

integral from 1 to 4 of ((3x^2+9x+1)/x)

\int_{1}^{4} (\frac{3 x ^{2} + 9 x + 1}{x}) d x

integral from 2 to 3 of 2/(x^3+x^2)

\int_{2}^{3} \frac{2}{x ^{3} + x ^{2}} d x

integral from-2 to 2 of (9-|x|^3)

\int_{- 2}^{2} (9 - ∣ x ∣^{3}) d x

integral from 0 to 6 of x/3

\int_{0}^{6} \frac{x}{3} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of x(x-7) ?
The integral from 0 to 3 of x(x-7) is -45/2