What is the integral from 2 to 7 of (x-5)^2 ?

The integral from 2 to 7 of (x-5)^2 is 35/3

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integral from 2 to 7 of (x-5)^2

\int_{2}^{7} (x - 5)^{2} d x

\frac{35}{3}

Decimal Notation

11.66666 \dots

Solution steps

\int_{2}^{7} (x - 5)^{2} d x

Expand

(x - 5)^{2} : x^{2} - 10 x + 25

= \int_{2}^{7} x^{2} - 10 x + 25 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}^{7} x^{2} d x - \int_{2}^{7} 10 x d x + \int_{2}^{7} 25 d x

\int_{2}^{7} x^{2} d x = \frac{335}{3}

\int_{2}^{7} 10 x d x = 225

\int_{2}^{7} 25 d x = 125

= \frac{335}{3} - 225 + 125

Simplify

\frac{335}{3} - 225 + 125 : \frac{35}{3}

= \frac{35}{3}

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What is the integral from 2 to 7 of (x-5)^2 ?
The integral from 2 to 7 of (x-5)^2 is 35/3