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Popular >

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

Solution

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

Solution

\frac{7}{6}

+1

Decimal

1.16666 \dots

Solution steps

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

Expand

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

= \int_{2}^{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_{2}^{3} 3 x d x - \int_{2}^{3} x^{2} d x

\int_{2}^{3} 3 x d x = \frac{15}{2}

\int_{2}^{3} x^{2} d x = \frac{19}{3}

= \frac{15}{2} - \frac{19}{3}

Simplify

\frac{15}{2} - \frac{19}{3} : \frac{7}{6}

= \frac{7}{6}

Graph

Popular Examples

integral from 5 to 10 of (10-x)/(25)

\int_{5}^{10} \frac{10 - x}{25} d x

integral from 0 to 2pi of-98sin^2(t)

\int_{0}^{2 π} - 98 sin^{2} (t) d t

integral from 0 to x of 2-t

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

integral from-2 to 1 of x^{-2}

\int_{- 2}^{1} x^{- 2} d x

integral from 0 to 1 of 10sqrt(x^2+1)

\int_{0}^{1} 10 x^{2} + 1 d x

Frequently Asked Questions (FAQ)

What is the integral from 2 to 3 of x(3-x) ?
The integral from 2 to 3 of x(3-x) is 7/6