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Popular >

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

Solution

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

Solution

21

Solution steps

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

Expand

(x - 2)^{2} : x^{2} - 4 x + 4

= \int_{- 2}^{1} x^{2} - 4 x + 4 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_{- 2}^{1} x^{2} d x - \int_{- 2}^{1} 4 x d x + \int_{- 2}^{1} 4 d x

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

\int_{- 2}^{1} 4 x d x = - 6

\int_{- 2}^{1} 4 d x = 12

= 3 - (- 6) + 12

Simplify

= 21

Graph

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Frequently Asked Questions (FAQ)

What is the integral from-2 to 1 of (x-2)^2 ?
The integral from-2 to 1 of (x-2)^2 is 21