MHB Double Integral Problem/ Surface Area of parametric surface

[Dizzy1]

Hi I'm doing a surface area problem with a parametric surface and I got the cross product but I can't figure out the double integral.

I found the solution online but with no explanation, so can someone explain how to solve this integral:

View attachment 2449

thank you!

 

[zzephod]

Hi I'm doing a surface area problem with a parametric surface and I got the cross product but I can't figure out the double integral.

I found the solution online but with no explanation, so can someone explain how to solve this integral:

View attachment 2449

thank you!

Because the inner integral is just a number you can immediately do the outer integral so:

$$\int_0^{\pi}\ \int_0^1\sqrt{1+u^2}du\ dv=\pi \int_0^1\sqrt{1+u^2}du$$

.