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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{343}{6}

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}

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

\int_{0}^{1} \frac{x}{( 2 x ^{2} + 1 ) ^{3}} d x

\int_{0}^{3} \frac{1}{x - 3} d x

\int_{0}^{1} 5 x^{4} d x

\int_{1}^{2} 15 x^{2} (x^{3} - 7)^{4} d x

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