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

  • #1
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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?
 

Answers and Replies

  • #2
HallsofIvy
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Yes, it is simple if you can write the boundary of the "blob" in terms of integrable functions! That's the hard part.
 
  • #3
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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?
 
  • #4
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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)
 

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