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Popular >

integral from 0 to 6 of (x-3)^2

Solution

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

Solution

18

Solution steps

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

Expand

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

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

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

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

\int_{0}^{6} 9 d x = 54

= 72 - 108 + 54

Simplify

= 18

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of (x-3)^2 ?
The integral from 0 to 6 of (x-3)^2 is 18