Question

determine the limits and evaluate..
∫∫x2y2dA
where f is a figure bounded by F lines y = 1, y = 2 and x = 0, x = y

Answer 1

that gives you the limits

Answer 2

it is easier to travel on y-axis because there is no sudden breaks

Answer 3

so \[0\le x\le y \qquad\text{&}\qquad1\le y\le2\]

Answer 4

if you are on the x-axis, you have to consider two pieces
A) \(1\le y\le2 \qquad\text{&}\qquad0\le x\le1\)
B) \(x\le y\le2 \qquad\text{&}\qquad1\le x\le2\)
and sum them

Answer 5

follow?

Answer 6

in x=y, the value of y will become a and 2?

Answer 7

"a"?

Answer 8

all points on the "x=y" line will have the same abscissa and ordinate

Answer 9

ah ok..

Answer 10

yup, in the problem, all you need are the limits

Answer 11

will i add these
A) 1≤y≤2&0≤x≤1
B) x≤y≤2&1≤x≤2 ??

Answer 12

use the first method its easier.

Answer 13

yes those are your two regions for the second method

Answer 14

x=0 to 1 and y= 1 to 2 ?

Answer 15

no
x=0 to y
and
y=1 to 2