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Popular >

integral from 0 to 3 of (x-3)^2

Solution

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

Solution

9

Solution steps

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

Expand

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

= \int_{0}^{3} 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}^{3} x^{2} d x - \int_{0}^{3} 6 x d x + \int_{0}^{3} 9 d x

\int_{0}^{3} x^{2} d x = 9

\int_{0}^{3} 6 x d x = 27

\int_{0}^{3} 9 d x = 27

= 9 - 27 + 27

Simplify

= 9

Graph

Popular Examples

integral from 1 to 3 of (x+1)^4

\int_{1}^{3} (x + 1)^{4} d x

integral from 2 to 7 of x/(x^2+1)

\int_{2}^{7} \frac{x}{x ^{2} + 1} d x

integral from-1 to 1 of 2y

\int_{- 1}^{1} 2 y d y

integral from 0 to 8 of 2/((x+2)^2)

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

integral from 1 to 2 of (m^2+1)/(m^3)

\int_{1}^{2} \frac{m ^{2} + 1}{m ^{3}} d m

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (x-3)^2 ?
The integral from 0 to 3 of (x-3)^2 is 9