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Popular >

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

Solution

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

Solution

\frac{125}{6}

+1

Solution steps

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

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

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

= \frac{125}{2} - \frac{125}{3}

Simplify

\frac{125}{2} - \frac{125}{3} : \frac{125}{6}

= \frac{125}{6}

Popular Examples

derivative of y^4-2x

\frac{d}{d x} (y^{4} - 2 x)

(\partial)/(\partial z)(xy^2)

\frac{\partial}{\partial z} (x y^{2})

(\partial)/(\partial x)(2xy-28x)

\frac{\partial}{\partial x} (2 x y - 28 x)

integral of (x^3+6x-2)/(x^4+6x^2)

\int \frac{x ^{3} + 6 x - 2}{x ^{4} + 6 x ^{2}} d x

integral of 5^{-8(x-7)}

\int 5^{- 8 (x - 7)} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of 5x-x^2 ?
The integral from 0 to 5 of 5x-x^2 is 125/6