What is the integral from 2 to 3 of x(x-2)(x+2) ?

The integral from 2 to 3 of x(x-2)(x+2) is 25/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{25}{4}

Decimal

6.25

Solution steps

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

Apply Integration By Parts

: [(x + 2) (\frac{x ^{3}}{3} - x^{2}) - \int \frac{x ^{3}}{3} - x^{2} d x]_{2}^{3}

= [(x + 2) (\frac{x ^{3}}{3} - x^{2}) - \int \frac{x ^{3}}{3} - x^{2} d x]_{2}^{3}

\int \frac{x ^{3}}{3} - x^{2} d x = \frac{x ^{4}}{12} - \frac{x ^{3}}{3}

= [(x + 2) (\frac{x ^{3}}{3} - x^{2}) - (\frac{x ^{4}}{12} - \frac{x ^{3}}{3})]_{2}^{3}

Simplify

[(x + 2) (\frac{x ^{3}}{3} - x^{2}) - (\frac{x ^{4}}{12} - \frac{x ^{3}}{3})]_{2}^{3} : [\frac{1}{4} x^{2} (x^{2} - 8)]_{2}^{3}

= [\frac{1}{4} x^{2} (x^{2} - 8)]_{2}^{3}

Compute the boundaries:

\frac{25}{4}

= \frac{25}{4}

x^{2} - 10 x + 4, (0)

\int \frac{1}{x ^{2} - 10 x + 34} d x

1 - 7 x^{2} y^{^{'}} = x

x \to 8 + lim (\frac{1}{x - 8})

\frac{\partial}{\partial x} (\frac{16}{x y})

What is the integral from 2 to 3 of x(x-2)(x+2) ?
The integral from 2 to 3 of x(x-2)(x+2) is 25/4