What is the integral from 2 to 9 of 3xsqrt(x^2-1) ?

The integral from 2 to 9 of 3xsqrt(x^2-1) is 320sqrt(5)-3sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 2 to 9 of 3xsqrt(x^2-1)

\int_{2}^{9} 3 x x^{2} - 1 d x

3205 - 33

Decimal

710.34560 \dots

Solution steps

\int_{2}^{9} 3 x x^{2} - 1 d x

Take the constant out:

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

= 3 \cdot \int_{2}^{9} x x^{2} - 1 d x

Apply u-substitution

= 3 \cdot \int_{3}^{45} u^{2} d u

Apply the Power Rule

= 3 [\frac{u ^{3}}{3}]_{3}^{45}

Compute the boundaries:

\frac{320 5}{3} - 3

= 3 (\frac{320 5}{3} - 3)

Simplify

= 3205 - 33

What is the integral from 2 to 9 of 3xsqrt(x^2-1) ?
The integral from 2 to 9 of 3xsqrt(x^2-1) is 320sqrt(5)-3sqrt(3)