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Popular >

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

Solution

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

Solution

\frac{125}{3}

+1

Decimal Notation

41.66666 \dots

Solution steps

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

Expand

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

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

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

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

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

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

Simplify

= \frac{125}{3}

Popular Examples

integral from pi/2 to 2pi of xsin(x)

\int_{\frac{π}{2}}^{2 π} x sin (x) d x

integral from-1 to 2 of 3^x

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

integral from 1 to 5 of (12(ln(x))^3)/x

\int_{1}^{5} \frac{12 ( ln ( x ) ) ^{3}}{x} d x

integral from-pi/2 to pi/2 of xcos(x)

\int_{- \frac{π}{2}}^{\frac{π}{2}} x cos (x) d x

integral from 0 to a of 1

\int_{0}^{a} 1 d x

Frequently Asked Questions (FAQ)

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