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 6 of (x-3)^2+2

Solution

\int_{0}^{6} (x - 3)^{2} + 2 d x

Solution

30

Solution steps

\int_{0}^{6} (x - 3)^{2} + 2 d x

Simplify

(x - 3)^{2} + 2 : x^{2} - 6 x + 11

= \int_{0}^{6} x^{2} - 6 x + 11 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}^{6} x^{2} d x - \int_{0}^{6} 6 x d x + \int_{0}^{6} 11 d x

\int_{0}^{6} x^{2} d x = 72

\int_{0}^{6} 6 x d x = 108

\int_{0}^{6} 11 d x = 66

= 72 - 108 + 66

Simplify

= 30

Graph

Popular Examples

integral from 1 to 5 of 1/((t-4)^2)

\int_{1}^{5} \frac{1}{( t - 4 ) ^{2}} d t

integral from 0 to 25 of 5sqrt(x)

\int_{0}^{25} 5 x d x

integral from 0 to 4 of (x^2)/4

\int_{0}^{4} \frac{x ^{2}}{4} d x

integral from-1 to 1 of (x^2+2x+1)

\int_{- 1}^{1} (x^{2} + 2 x + 1) d x

integral from 0 to pi/2 of 4cos^4(x)

\int_{0}^{\frac{π}{2}} 4 cos^{4} (x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of (x-3)^2+2 ?
The integral from 0 to 6 of (x-3)^2+2 is 30