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Popular Calculus >

integral from 0 to 5 of (4x-x^2)

Solution

\int_{0}^{5} (4 x - x^{2}) d x

Solution

\frac{25}{3}

+1

Decimal

8.33333 \dots

Solution steps

\int_{0}^{5} 4 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} 4 x d x - \int_{0}^{5} x^{2} d x

\int_{0}^{5} 4 x d x = 50

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

= 50 - \frac{125}{3}

Simplify

50 - \frac{125}{3} : \frac{25}{3}

= \frac{25}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of (4x-x^2) ?
The integral from 0 to 5 of (4x-x^2) is 25/3