en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

area 3/x ,12x, 1/3 x

Solution

area

\frac{3}{x}, 12 x, \frac{1}{3} x

Solution

6 ln (6)

+1

Decimal Notation

10.75055 \dots

Solution steps

To find the intersection points solve

f_{i} (x) = f_{j} (x)

\frac{3}{x} = 12 x : x = \frac{1}{2}, x = - \frac{1}{2}

\frac{3}{x} = \frac{1}{3} x : x = 3, x = - 3

12 x = \frac{1}{3} x : x = 0

= \int_{- 3}^{- \frac{1}{2}} ∣ f_{1} (x) - f_{3} (x) ∣ d x + \int_{- \frac{1}{2}}^{0} ∣ f_{3} (x) - f_{2} (x) ∣ d x + \int_{0}^{\frac{1}{2}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{\frac{1}{2}}^{3} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- 3}^{- \frac{1}{2}} \frac{3}{x} - \frac{1}{3} x d x + \int_{- \frac{1}{2}}^{0} \frac{1}{3} x - 12 x d x + \int_{0}^{\frac{1}{2}} 12 x - \frac{1}{3} x d x + \int_{\frac{1}{2}}^{3} \frac{3}{x} - \frac{1}{3} x d x

\int_{- 3}^{- \frac{1}{2}} \frac{3}{x} - \frac{1}{3} x d x = 3 ln (6) - \frac{35}{24}

\int_{- \frac{1}{2}}^{0} \frac{1}{3} x - 12 x d x = \frac{35}{24}

\int_{0}^{\frac{1}{2}} 12 x - \frac{1}{3} x d x = \frac{35}{24}

\int_{\frac{1}{2}}^{3} \frac{3}{x} - \frac{1}{3} x d x = 3 ln (6) - \frac{35}{24}

= 3 ln (6) - \frac{35}{24} + \frac{35}{24} + \frac{35}{24} + 3 ln (6) - \frac{35}{24}

Simplify

= 6 ln (6)

Popular Examples

integral of rsqrt(1+4r^2)

\int r 1 + 4 r^{2} d r

tangent of f(x)=cos(x),\at x= pi/4 tangent of

f (x) = cos (x), at x = \frac{π}{4}

derivative of x5^x derivative of

x 5^{x}

tangent of 2/(sqrt(x)),\at x=3 tangent of

\frac{2}{x}, at x = 3

integral of 2/(2x+1)

\int \frac{2}{2 x + 1} d x

Frequently Asked Questions (FAQ)

What is area 3/x ,12x, 1/3 x ?
The answer to area 3/x ,12x, 1/3 x is 6ln(6)