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Popular >

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

Solution

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

Solution

\frac{152}{3}

+1

Decimal

50.66666 \dots

Solution steps

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

Expand

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

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 12 x d x = 24

\int_{0}^{2} 36 d x = 72

= \frac{8}{3} - 24 + 72

Simplify

\frac{8}{3} - 24 + 72 : \frac{152}{3}

= \frac{152}{3}

Graph

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\int_{2}^{4} 2 x - 4 d x

integral from 1 to 2 of 1/(sqrt(1+x))

\int_{1}^{2} \frac{1}{1 + x} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (x-6)^2 ?
The integral from 0 to 2 of (x-6)^2 is 152/3