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Popular >

integral from 3 to 6 of (x-4)^2

Solution

\int_{3}^{6} (x - 4)^{2} d x

Solution

3

Solution steps

\int_{3}^{6} (x - 4)^{2} d x

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{3}^{6} x^{2} - 8 x + 16 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_{3}^{6} x^{2} d x - \int_{3}^{6} 8 x d x + \int_{3}^{6} 16 d x

\int_{3}^{6} x^{2} d x = 63

\int_{3}^{6} 8 x d x = 108

\int_{3}^{6} 16 d x = 48

= 63 - 108 + 48

Simplify

= 3

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 3 to 6 of (x-4)^2 ?
The integral from 3 to 6 of (x-4)^2 is 3