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Popular >

integral from 0 to 3 of (x-6)^2

Solution

\int_{0}^{3} (x - 6)^{2} d x

Solution

63

Solution steps

\int_{0}^{3} (x - 6)^{2} d x

Expand

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

= \int_{0}^{3} 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_{0}^{3} x^{2} d x - \int_{0}^{3} 12 x d x + \int_{0}^{3} 36 d x

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

\int_{0}^{3} 12 x d x = 54

\int_{0}^{3} 36 d x = 108

= 9 - 54 + 108

Simplify

= 63

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

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\int_{1}^{4} 9 x^{- \frac{3}{2}} d x

integral from 3 to x^2 of ln(x)

\int_{3}^{x^{2}} ln (x) d x

integral from 2 to 8 of x^2-2x-15

\int_{2}^{8} x^{2} - 2 x - 15 d x

integral from 2 to 3 of x^2ln(x)

\int_{2}^{3} x^{2} ln (x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (x-6)^2 ?
The integral from 0 to 3 of (x-6)^2 is 63