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 8 of (8-x)^2

Solution

\int_{0}^{8} (8 - x)^{2} d x

Solution

\frac{512}{3}

+1

Decimal Notation

170.66666 \dots

Solution steps

\int_{0}^{8} (8 - x)^{2} d x

Expand

(8 - x)^{2} : 64 - 16 x + x^{2}

= \int_{0}^{8} 64 - 16 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}^{8} 64 d x - \int_{0}^{8} 16 x d x + \int_{0}^{8} x^{2} d x

\int_{0}^{8} 64 d x = 512

\int_{0}^{8} 16 x d x = 512

\int_{0}^{8} x^{2} d x = \frac{512}{3}

= 512 - 512 + \frac{512}{3}

Simplify

= \frac{512}{3}

Popular Examples

integral of (cos(t))/(sin^2(t))

\int \frac{cos ( t )}{sin ^{2} ( t )} d t

integral of arcsin(7x)

\int arcsin (7 x) d x

(\partial)/(\partial y)(3ycos(pix)+2xz)

\frac{\partial}{\partial y} (3 y cos (π x) + 2 x z)

y^'= 3/x (y^2+y),y(4)=2

y^{^{'}} = \frac{3}{x} (y^{2} + y), y (4) = 2

integral of 1/v

\int \frac{1}{v} d v

Frequently Asked Questions (FAQ)

What is the integral from 0 to 8 of (8-x)^2 ?
The integral from 0 to 8 of (8-x)^2 is 512/3