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 4 of (x-3)^2

Solution

\int_{0}^{4} (x - 3)^{2} d x

Solution

\frac{28}{3}

+1

Decimal

9.33333 \dots

Solution steps

\int_{0}^{4} (x - 3)^{2} d x

Expand

(x - 3)^{2} : x^{2} - 6 x + 9

= \int_{0}^{4} x^{2} - 6 x + 9 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} 6 x d x + \int_{0}^{4} 9 d x

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

\int_{0}^{4} 6 x d x = 48

\int_{0}^{4} 9 d x = 36

= \frac{64}{3} - 48 + 36

Simplify

\frac{64}{3} - 48 + 36 : \frac{28}{3}

= \frac{28}{3}

Graph

Popular Examples

integral from 0 to pi/2 of e^{-4x}cos(x)

integral from 4 to x of t^5

integral from 0 to 4 of (5-5x)

integral from 3 to 6 of 10000e^{0.02x}

integral from-infinity to 0 of-xe^{-x^2}

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of (x-3)^2 ?
The integral from 0 to 4 of (x-3)^2 is 28/3