Processing math: 84%
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

7.6E

( \newcommand{\kernel}{\mathrm{null}\,}\)

Exercise 1: Mass

In the following exercises, the region R occupied by a lamina is shown in a graph. Find the mass of R with the density function ρ.

1. R is the triangular region with vertices (0,0), (0,3), and (6,0); ρ(x,y)=xy.

A right triangle bounded by the x and y axes and the line y = negative x/2 + 3.

Answer

272

3. R is the triangular region with vertices (0,0), (1,1), and (0,5); ρ(x,y)=x+y.

A triangle bounded by the y axis, the line x = y, and the line y = negative 4x + 5.

4. R is the rectangular region with vertices (0,0), (0,3), (6,3) and (6,0); ρ(x,y)=xy.

A rectangle bounded by the x and y axes and the lines x = 6 and y = 3.

Answer

242

5. R is the rectangular region with vertices (0,1), (0,3), (3,3) and (3,1); ρ(x,y)=x2y.

A rectangle bounded by the y axis, the lines y = 1 and 3, and the line x = 3.

6. R is the trapezoidal region determined by the lines y=14x+52, y=0, y=2, and x=0; ρ(x,y)=3xy.

A trapezoid bounded by the x and y axes, the line y = 2, and the line y = negative x/4 + 2.5.

Answer

76

7. R is the trapezoidal region determined by the lines y=0, y=1, y=x and y=x+3; ρ(x,y)=2x+y.

A trapezoid bounded by the x axis, the line y = 1, the line y = x, and the line y = negative x + 3.

8. R is the disk of radius 2 centered at (1,2); ρ(x,y)=x2+y22x4y+5.


This page titled 7.6E is shared under a not declared license and was authored, remixed, and/or curated by Pamini Thangarajah.

Support Center

How can we help?