Hard Integration Question:

[helloooooo1345]

I am really struggling integrating the above equation - I am doing it as part of a project to find the surface area of a Pringle.
I would greatly appreciate it if someone could walk me through the method of how to integrate this. I will use limits so it will become a definite integral - these limits are 3.5 and -3.5 for y and 2.8 and -2.8 for x.
Thank you

 

[Deleted member 4993]

View attachment 22210
I am really struggling integrating the above equation - I am doing it as part of a project to find the surface area of a Pringle.
I would greatly appreciate it if someone could walk me through the method of how to integrate this. I will use limits so it will become a definite integral - these limits are 3.5 and -3.5 for y and 2.8 and -2.8 for x.
Thank you

your integrand is of the form √(A^2*x^2 + B^2*y^2 +1).

Convert to polar-coordinate by substituting:

A*x = r * sin(Θ)........... and............... B*y = r * cos(Θ)

Make sure to transform 'dy' & 'dx' and the corresponding limits.

 

[Steven G]

[MATH]\int x^2dx = \dfrac{x^3}{3} + c, \int y^2dx = xy^2 + c[/MATH]This should be helpful.