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Popular >

integral from-1 to 5 of (x-2)^2

Solution

\int_{- 1}^{5} (x - 2)^{2} d x

Solution

18

Solution steps

\int_{- 1}^{5} (x - 2)^{2} d x

Expand

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

= \int_{- 1}^{5} 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_{- 1}^{5} x^{2} d x - \int_{- 1}^{5} 4 x d x + \int_{- 1}^{5} 4 d x

\int_{- 1}^{5} x^{2} d x = 42

\int_{- 1}^{5} 4 x d x = 48

\int_{- 1}^{5} 4 d x = 24

= 42 - 48 + 24

Simplify

= 18

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Frequently Asked Questions (FAQ)

What is the integral from-1 to 5 of (x-2)^2 ?
The integral from-1 to 5 of (x-2)^2 is 18