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Popular >

integral from 0 to 3 of (5x-x^2)

Solution

\int_{0}^{3} (5 x - x^{2}) d x

Solution

\frac{27}{2}

+1

Decimal Notation

13.5

Solution steps

\int_{0}^{3} 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}^{3} 5 x d x - \int_{0}^{3} x^{2} d x

\int_{0}^{3} 5 x d x = \frac{45}{2}

\int_{0}^{3} x^{2} d x = 9

= \frac{45}{2} - 9

Simplify

\frac{45}{2} - 9 : \frac{27}{2}

= \frac{27}{2}

Popular Examples

integral of x^2ln(ex)

\int x^{2} ln (e x) d x

y^{''}-4y^'+4y=t^{-7}e^{2t}

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{- 7} e^{2 t}

integral of 1/((1-y)(2-y))

\int \frac{1}{( 1 - y ) ( 2 - y )} d y

laplacetransform f(s)=2te^{-5t}laplace transform

f (s) = 2 t e^{- 5 t}

area f(x)=x^2+2x,[1,2]area

f (x) = x^{2} + 2 x, [1, 2]

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (5x-x^2) ?
The integral from 0 to 3 of (5x-x^2) is 27/2