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Popular Calculus >

integral from 0 to 3 of (x-9)^2

Solution

\int_{0}^{3} (x - 9)^{2} d x

Solution

171

Solution steps

\int_{0}^{3} (x - 9)^{2} d x

Expand

(x - 9)^{2} : x^{2} - 18 x + 81

= \int_{0}^{3} x^{2} - 18 x + 81 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} 18 x d x + \int_{0}^{3} 81 d x

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

\int_{0}^{3} 18 x d x = 81

\int_{0}^{3} 81 d x = 243

= 9 - 81 + 243

Simplify

= 171

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (x-9)^2 ?
The integral from 0 to 3 of (x-9)^2 is 171