What is the integral from 1 to 2 of 4xsqrt(3x^2-1) ?

The integral from 1 to 2 of 4xsqrt(3x^2-1) is (2(22sqrt(11)-4sqrt(2)))/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of 4xsqrt(3x^2-1)

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

\frac{2 ( 22 11 - 4 2 )}{9}

Decimal Notation

14.95753 \dots

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int_{2}^{11} \frac{u}{6} d u

= 4 \cdot \int_{2}^{11} \frac{u}{6} d u

Take the constant out:

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

= 4 \cdot \frac{1}{6} \cdot \int_{2}^{11} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{11}

= 4 \cdot \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{11}

Simplify

4 \cdot \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{11} : \frac{2}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{11}

= \frac{2}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{11}

Compute the boundaries:

\frac{22 11 - 4 2}{3}

= \frac{2}{3} \cdot \frac{22 11 - 4 2}{3}

Simplify

= \frac{2 ( 22 11 - 4 2 )}{9}

f (x) = (π x)^{2}

y = e^{x} 2^{x}

y = 2 x^{2}, x = 2, y = 0

sec^{2} (t)

ln (x^{9})

What is the integral from 1 to 2 of 4xsqrt(3x^2-1) ?
The integral from 1 to 2 of 4xsqrt(3x^2-1) is (2(22sqrt(11)-4sqrt(2)))/9