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Popular >

integral from 0 to 5 of (x-5)^2

Solution

\int_{0}^{5} (x - 5)^{2} d x

Solution

\frac{125}{3}

+1

Decimal

41.66666 \dots

Solution steps

\int_{0}^{5} (x - 5)^{2} d x

Expand

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

= \int_{0}^{5} 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_{0}^{5} x^{2} d x - \int_{0}^{5} 10 x d x + \int_{0}^{5} 25 d x

\int_{0}^{5} x^{2} d x = \frac{125}{3}

\int_{0}^{5} 10 x d x = 125

\int_{0}^{5} 25 d x = 125

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

Simplify

= \frac{125}{3}

Graph

Popular Examples

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

integral from 1 to 10 of 1

\int_{1}^{10} 1

integral from 0 to 2 of (2x+3)^2

\int_{0}^{2} (2 x + 3)^{2} d x

integral from 1 to 2 of (30x^3+6/(x^2))

\int_{1}^{2} (30 x^{3} + \frac{6}{x ^{2}}) d x

integral from 1 to 4 of 14x^{5/2}

\int_{1}^{4} 14 x^{\frac{5}{2}} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of (x-5)^2 ?
The integral from 0 to 5 of (x-5)^2 is 125/3