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Popular Calculus >

integral from 1 to 5 of (5-x)^2

Solution

\int_{1}^{5} (5 - x)^{2} d x

Solution

\frac{64}{3}

+1

Decimal

21.33333 \dots

Solution steps

\int_{1}^{5} (5 - x)^{2} d x

Expand

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

= \int_{1}^{5} 25 - 10 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}^{5} 25 d x - \int_{1}^{5} 10 x d x + \int_{1}^{5} x^{2} d x

\int_{1}^{5} 25 d x = 100

\int_{1}^{5} 10 x d x = 120

\int_{1}^{5} x^{2} d x = \frac{124}{3}

= 100 - 120 + \frac{124}{3}

Simplify

100 - 120 + \frac{124}{3} : \frac{64}{3}

= \frac{64}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 1 to 5 of (5-x)^2 ?
The integral from 1 to 5 of (5-x)^2 is 64/3