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 4 of (x-4)^2

Solution

\int_{0}^{4} (x - 4)^{2} d x

Solution

\frac{64}{3}

+1

Decimal Notation

21.33333 \dots

Solution steps

\int_{0}^{4} (x - 4)^{2} d x

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{0}^{4} x^{2} - 8 x + 16 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}^{4} x^{2} d x - \int_{0}^{4} 8 x d x + \int_{0}^{4} 16 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 8 x d x = 64

\int_{0}^{4} 16 d x = 64

= \frac{64}{3} - 64 + 64

Simplify

= \frac{64}{3}

Popular Examples

(\partial)/(\partial x)(-sin(y))

\frac{\partial}{\partial x} (- sin (y))

limit as x approaches 1-of ln(x)

x \to 1 - lim (ln (x))

(xdy)/(dx)+2y=3

\frac{x d y}{d x} + 2 y = 3

y^{''}+3y^'=2t^4+t^2e^{-3t}+sin(3t)

y^{^{''}} + 3 y^{^{'}} = 2 t^{4} + t^{2} e^{- 3 t} + sin (3 t)

y^{^{'}} = x y^{2} + 2 x y

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of (x-4)^2 ?
The integral from 0 to 4 of (x-4)^2 is 64/3