 Sun K.

# Find the mass of the plate with density?

Find the mass of the plate with density p(x, y)=ky, where k is a positive constant and R is the region bounded by y=x^2 and x=y^2.

Sun K.

Where did you get 0 to 1?

Report

05/04/13 tutor

Hey Sun!  Visualize a 1x1 box. The region of overlapping "U-curves" or parabolas is like a pistachio touching the origin at the "southwest" corner running to the NW corner at (1,1). The overlap in so thin that it's a sliver of the box area.

Report

05/04/13 Grigori S.

This is the explanation why these two curves have two points of  intersection (0,0) and (1,1).

If   y = x^2 and x = y^2 then x^2 = y^4 and we can substitute x^2 into the first equation. We will obtain

y = y^4    or y^4 - y = 0

We can factor this equation and write:

y(y^3 -1)= y(y-1)(y^2 +y+1) = 0

First two factors give us y = 0 and y = 1 as solutions of the equation. Thus x = 0 if y=0 and x = 1 if y=1.

This is visible from graphs of the functions. The third term y^2 +y +1 has only

complex roots and can't be used here.

Report

05/05/13 Grigori S.

This is the explanation why these two curves have two points of  intersection (0,0) and (1,1).

If   y = x^2 and x = y^2 then x^2 = y^4 and we can substitute x^2 into the first equation. We will obtain

y = y^4    or y^4 - y = 0

We can factor this equation and write:

y(y^3 -1)= y(y-1)(y^2 +y+1) = 0

First two factors give us y = 0 and y = 1 as solutions of the equation. Thus x = 0 if y=0 and x = 1 if y=1.

This is visible from graphs of the functions. The third term y^2 +y +1 has only

complex roots and can't be used here.

Report

05/05/13

## 2 Answers By Expert Tutors

By: Tutor
New to Wyzant

Certified Physics and Math Teacher G.S. Tutor
4.6 (13)

Certified High School AP Calculus and Physics Teacher Robert J.

The intersection of y=x^2 and x=y^2 is at x = 0, and 1. So, the lower limit is 0, and the upper limit is 1.

Report

05/06/13

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.
Most questions answered within 4 hours.

#### OR

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.