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Popular >

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

Solution

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

Solution

\frac{1}{3}

+1

Decimal

0.33333 \dots

Solution steps

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

Expand

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

= \int_{2}^{3} 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}^{3} x^{2} d x - \int_{2}^{3} 4 x d x + \int_{2}^{3} 4 d x

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 4 x d x = 10

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

= \frac{19}{3} - 10 + 4

Simplify

\frac{19}{3} - 10 + 4 : \frac{1}{3}

= \frac{1}{3}

Graph

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\int_{- π}^{0} sin (3 x) d x

integral from infinity to 0 of xe^x

\int_{\infty}^{0} x e^{x} d x

integral from x to 0 of e^{-4t}

\int_{x}^{0} e^{- 4 t} d t

integral from-1 to 2 of-x

\int_{- 1}^{2} - x d x

integral from 1 to 6 of (4x^2-3)/(x^3)

\int_{1}^{6} \frac{4 x ^{2} - 3}{x ^{3}} d x

Frequently Asked Questions (FAQ)

What is the integral from 2 to 3 of (x-2)^2 ?
The integral from 2 to 3 of (x-2)^2 is 1/3