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Popular >

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

Solution

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

Solution

\frac{9}{2}

+1

Solution steps

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

\int_{0}^{3} 3 x d x = \frac{27}{2}

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

= \frac{27}{2} - 9

Simplify

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

= \frac{9}{2}

Popular Examples

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3 e^{- 2 t} cos (3 t)

limit as x approaches 3 of 1/(3-x)

x \to 3 lim (\frac{1}{3 - x})

y^'=(4x^4e^{y/x}+x^2y^2)/(x^3y)

y^{^{'}} = \frac{4 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

integral of x^3sqrt(x^2-81)

\int x^{3} x^{2} - 81 d x

integral of (cot^3(x))/5

\int \frac{cot ^{3} ( x )}{5} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (3x-x^2) ?
The integral from 0 to 3 of (3x-x^2) is 9/2