What is the integral from 2 to 3 of 12(x^2-4)^5x ?

The integral from 2 to 3 of 12(x^2-4)^5x is 15625

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 12(x^2-4)^5x

\int_{2}^{3} 12 (x^{2} - 4)^{5} x d x

15625

Solution steps

\int_{2}^{3} 12 (x^{2} - 4)^{5} x d x

Take the constant out:

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

= 12 \cdot \int_{2}^{3} (x^{2} - 4)^{5} x d x

Apply u-substitution

: \int_{0}^{5} \frac{u ^{5}}{2} d u

= 12 \cdot \int_{0}^{5} \frac{u ^{5}}{2} d u

Take the constant out:

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

= 12 \cdot \frac{1}{2} \cdot \int_{0}^{5} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{0}^{5}

= 12 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{0}^{5}

Simplify

12 \cdot \frac{1}{2} [\frac{u ^{6}}{6}]_{0}^{5} : 6 [\frac{u ^{6}}{6}]_{0}^{5}

= 6 [\frac{u ^{6}}{6}]_{0}^{5}

Compute the boundaries:

\frac{15625}{6}

= 6 \cdot \frac{15625}{6}

Simplify

= 15625

\int_{1}^{2} x^{6} d x

\int_{1}^{4} 3 x^{2} - \frac{x ^{3}}{4} d x

\int_{1}^{2} sin (x^{2}) d x

\int_{10}^{y} \frac{10}{x ^{2}} d x

\int_{0}^{π} 3 x sin (2 x) d x

What is the integral from 2 to 3 of 12(x^2-4)^5x ?
The integral from 2 to 3 of 12(x^2-4)^5x is 15625