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Popular Calculus >

integral from 5 to 8 of (x-6)^2

Solution

\int_{5}^{8} (x - 6)^{2} d x

Solution

3

Solution steps

\int_{5}^{8} (x - 6)^{2} d x

Expand

(x - 6)^{2} : x^{2} - 12 x + 36

= \int_{5}^{8} x^{2} - 12 x + 36 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_{5}^{8} x^{2} d x - \int_{5}^{8} 12 x d x + \int_{5}^{8} 36 d x

\int_{5}^{8} x^{2} d x = 129

\int_{5}^{8} 12 x d x = 234

\int_{5}^{8} 36 d x = 108

= 129 - 234 + 108

Simplify

= 3

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 5 to 8 of (x-6)^2 ?
The integral from 5 to 8 of (x-6)^2 is 3