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Popular >

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

Solution

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

Solution

\frac{9}{2}

+1

Decimal Notation

4.5

Solution steps

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

Expand

x (3 - x) : 3 x - x^{2}

= \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

integral of 2x^3(t^4-3)^5

\int 2 x^{3} (t^{4} - 3)^{5} d x

inverse oflaplace 3/((s+1)(s+2))inverse laplace

\frac{3}{( s + 1 ) ( s + 2 )}

integral of (14x-11)/((2x-3)(x+1))

\int \frac{14 x - 11}{( 2 x - 3 ) ( x + 1 )} d x

integral of ln(y+1)

\int ln (y + 1) d y

derivative of (s+3)/(4s^2+5)derivative of

\frac{s + 3}{4 s ^{2} + 5}

Frequently Asked Questions (FAQ)

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