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Popular >

integral from 0 to 2 of x(x-7)

Solution

\int_{0}^{2} x (x - 7) d x

Solution

- \frac{34}{3}

+1

Decimal

- 11.33333 \dots

Solution steps

\int_{0}^{2} x (x - 7) d x

Expand

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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 7 x d x = 14

= \frac{8}{3} - 14

Simplify

\frac{8}{3} - 14 : - \frac{34}{3}

= - \frac{34}{3}

Graph

Popular Examples

integral from 0 to 5 of |10-9x-7x^2|

\int_{0}^{5} 10 - 9 x - 7 x^{2} d x

integral from 0 to 2y of e^{y^2}

\int_{0}^{2 y} e^{y^{2}} d y

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

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

integral from (3pi)/2 to pi/2 of cos(x)

\int_{\frac{3 π}{2}}^{\frac{π}{2}} cos (x) d x

integral from 0 to pi/2 of sin^4(2x)

\int_{0}^{\frac{π}{2}} sin^{4} (2 x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x(x-7) ?
The integral from 0 to 2 of x(x-7) is -34/3