- #1
naggy
- 60
- 0
I'm supposed to prove that
[tex]\int\int_{S}^{}\ f(ax + by + c) \, dA \ =2 \int_{-1}^{1} \sqrt{1 - u^2} f(u\sqrt{a^2 + b^2} + c) \, du[/tex]
Where S is the disk x^2 + y^2 <= 1. It is also given that a^2 + b^2 is not zero
I can´t use polar coordinates and I can´t see how you simplify the surface S in any other way. What is the change of variable and why?
[tex]\int\int_{S}^{}\ f(ax + by + c) \, dA \ =2 \int_{-1}^{1} \sqrt{1 - u^2} f(u\sqrt{a^2 + b^2} + c) \, du[/tex]
Where S is the disk x^2 + y^2 <= 1. It is also given that a^2 + b^2 is not zero
I can´t use polar coordinates and I can´t see how you simplify the surface S in any other way. What is the change of variable and why?