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Popular Calculus >

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

Solution

\int_{1}^{3} (3 - x)^{2} d x

Solution

\frac{8}{3}

+1

Decimal

2.66666 \dots

Solution steps

\int_{1}^{3} (3 - x)^{2} d x

Expand

(3 - x)^{2} : 9 - 6 x + x^{2}

= \int_{1}^{3} 9 - 6 x + x^{2} 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_{1}^{3} 9 d x - \int_{1}^{3} 6 x d x + \int_{1}^{3} x^{2} d x

\int_{1}^{3} 9 d x = 18

\int_{1}^{3} 6 x d x = 24

\int_{1}^{3} x^{2} d x = \frac{26}{3}

= 18 - 24 + \frac{26}{3}

Simplify

18 - 24 + \frac{26}{3} : \frac{8}{3}

= \frac{8}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 1 to 3 of (3-x)^2 ?
The integral from 1 to 3 of (3-x)^2 is 8/3