en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

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

Solution

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

Solution

\frac{343}{3}

+1

Decimal

114.33333 \dots

Solution steps

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

Expand

(7 - x)^{2} : 49 - 14 x + x^{2}

= \int_{0}^{7} 49 - 14 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} 49 d x - \int_{0}^{7} 14 x d x + \int_{0}^{7} x^{2} d x

\int_{0}^{7} 49 d x = 343

\int_{0}^{7} 14 x d x = 343

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

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

Simplify

= \frac{343}{3}

Graph

Popular Examples

derivative of (ln(x)/(x^2))

(\partial)/(\partial x)(((2x+y))/(x+2y))

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

integral of+xln(x)

area e^{4x},e^{8x},x=1

Frequently Asked Questions (FAQ)

What is the integral from 0 to 7 of (7-x)^2 ?
The integral from 0 to 7 of (7-x)^2 is 343/3