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Popular Calculus >

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

Solution

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

Solution

\frac{8}{3}

+1

Decimal

2.66666 \dots

Solution steps

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

Expand

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

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

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 4 x d x = 24

\int_{2}^{4} 4 d x = 8

= \frac{56}{3} - 24 + 8

Simplify

\frac{56}{3} - 24 + 8 : \frac{8}{3}

= \frac{8}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 2 to 4 of (x-2)^2 ?
The integral from 2 to 4 of (x-2)^2 is 8/3