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Popular >

integral from 0 to 7 of 7x-x^2

Solution

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

Solution

\frac{343}{6}

+1

Decimal

57.16666 \dots

Solution steps

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

\int_{0}^{7} 7 x d x = \frac{343}{2}

\int_{0}^{7} x^{2} d x = \frac{343}{3}

= \frac{343}{2} - \frac{343}{3}

Simplify

\frac{343}{2} - \frac{343}{3} : \frac{343}{6}

= \frac{343}{6}

Graph

Popular Examples

integral from 0 to 1 of 2x^3

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

integral from 2 to 4 of |x^2-2x-3|

\int_{2}^{4} x^{2} - 2 x - 3 d x

integral from-pi to pi of xcos(x)

\int_{- π}^{π} x cos (x) d x

integral from 0 to pi/2 of x

\int_{0}^{\frac{π}{2}} x d x

integral from-1 to 2 of 2x

\int_{- 1}^{2} 2 x d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 7 of 7x-x^2 ?
The integral from 0 to 7 of 7x-x^2 is 343/6