What is the integral from-3 to-2 of 2x(4-x^2)^3 ?

The integral from-3 to-2 of 2x(4-x^2)^3 is 625/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-3 to-2 of 2x(4-x^2)^3

\int_{- 3}^{- 2} 2 x (4 - x^{2})^{3} d x

\frac{625}{4}

Decimal

156.25

Solution steps

\int_{- 3}^{- 2} 2 x (4 - x^{2})^{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{- 3}^{- 2} x (4 - x^{2})^{3} d x

Apply u-substitution

= 2 \cdot \int_{- 5}^{0} - \frac{u ^{3}}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 (- \frac{1}{2} \cdot \int_{- 5}^{0} u^{3} d u)

Apply the Power Rule

= 2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 5}^{0})

Simplify

2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{- 5}^{0}) : - [\frac{u ^{4}}{4}]_{- 5}^{0}

= - [\frac{u ^{4}}{4}]_{- 5}^{0}

Compute the boundaries:

- \frac{625}{4}

= - (- \frac{625}{4})

Simplify

= \frac{625}{4}

What is the integral from-3 to-2 of 2x(4-x^2)^3 ?
The integral from-3 to-2 of 2x(4-x^2)^3 is 625/4