You have go integrate along the curve [tex]y= x^4, not just replace y by . If [tex]y= x^{4}, then , not just "dx"

[/quote] X=0

0

I then put in y=x to get ∫ (5x-7x^2)dx for this I get a value of -1/6

X=1

When combined these two values equal 1/5.

Then according to Green’s thm this should equal

1 y=x

∫ ∫ {d(y-4x²)/dx – d(4x-3y²)/dy}dydx

X=0 y=x4

= ∫∫ (6y-8x)dydx = ∫ [3y^2-8xy] between y=x and y=x4

1

I get this equal to ∫(3x^2-8x^2-3x^8+8x^5)dx

X=0

Which I get as [(-5x^3)/3-(3x^9)/9+(8x^6)/6] which equals -5/3-3/9+8/6 = -2/3 ≠ 11/30

if you can spot where I’ve gone wrong or tell me what answer I should be looking for is it would be much appreciated thanks.[/QUOTE]