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Popular >

integral from 0 to 3 of (x-1)^2

Solution

\int_{0}^{3} (x - 1)^{2} d x

Solution

3

Solution steps

\int_{0}^{3} (x - 1)^{2} d x

Expand

(x - 1)^{2} : x^{2} - 2 x + 1

= \int_{0}^{3} x^{2} - 2 x + 1 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} 2 x d x + \int_{0}^{3} 1 d x

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

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

\int_{0}^{3} 1 d x = 3

= 9 - 9 + 3

Simplify

= 3

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (x-1)^2 ?
The integral from 0 to 3 of (x-1)^2 is 3