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]

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

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)