Is there someway to find the exact area of a blob using integrals?

questionpost

Someone told me Isaac Newton developed some infinitesimal triangle series to find the area of a random blob, but I think there might be some way to do it this way by drawing many lines from a central point to the edge, although that would make more of a pie slice, but is there some way to calculate the area of that pie slice using relative integrals?

HallsofIvy

Yes, it is simple if you can write the boundary of the "blob" in terms of integrable functions! That's the hard part.

questionpost

But what about it being in the shape of a pie slice? The range is just from x1 to x1?

Jorriss

A pie slice would be simple. You integrate in polar coordinates over the radius and angle. The boundaries are then (assuming a normal slice of pie): radius (0,r_o) and angle (0, theta)