Finding the area under a curve

[Luke77]

I'm trying to find the area of some shape with a straight line for the bottom, two curves on the sides and a straight top. Let's say I can only use calculus-like math. I can turn it on it's side and put it on a graph, but now there's now formula for the curved lines. What do I do? Do I split it into sections?

 

[voko]

Yes, split it into sections that are easy to integrate. Total area is the sum of the sectorial areas.