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## Homework Statement

This is a 2 part question. I'm fine with the first part but the 2nd part I'm struggling with.

The first part asks us to calculate the double integral,

[itex]\int\int[/itex]

_{D}x

^{2}dA

for, D = {(x,y)|0≤ x ≤1, x≤ y ≤1}

For this part I got an answer of 1/4.

For the 2nd part we introduce a new coordinate system for D,

x = 1-st, 0≤ s ≤1

y = s, 0≤ t ≤1

## The Attempt at a Solution

[itex]\int\int[/itex]

_{D}x

^{2}dA

= [itex]\int_0^1\int_0^1[/itex](1-st)

^{2}dt ds

= [itex]\int_0^1\int_0^1[/itex](1-2st+s

^{2}t

^{2})dt ds

= [itex]\int_0^1[/itex]t-st

^{2}+[itex]\frac{1}{3}[/itex]s

^{2}t

^{3}ds, from t=0 to t=1

= [itex]\int_0^1[/itex]1-s+[itex]\frac{1}{3}[/itex]s

^{2}ds

= s-[itex]\frac{1}{2}[/itex]s

^{2}+[itex]\frac{1}{9}[/itex]s

^{3}, from s=0 to s=1

= 1-[itex]\frac{1}{2}[/itex]+[itex]\frac{1}{9}[/itex]

= [itex]\frac{11}{18}[/itex]

I feel like,

dA [itex]\neq[/itex] dt ds

I'm not sure what it equals though. I thought I could use polar coordinates but I don't have a constant radius.