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Integration problem, calculus or no calculus?
See graph of 2 functions, √(1 - (x -1)² and x√(1 - (x -1)²
http://i254.photobucket.com/albums/hh120/Scythian1...
Prove that they have the same area. Maybe you can do this without calculus?
√(1 - (x -1)²) and x√(1 - (x -1)²), that is. A semicircle and a bent semicircle.
Having an easy time, Quadrilerator?
1 Answer
- QuadrilleratorLv 58 years agoFavorite Answer
The difference between the two functions is (x-1)√(1 - (x -1)²), which is an odd function with respect to the line x=1. Thus the integral from 1-a to 1+a of this difference is 0, so that the difference in the area between the two functions from 0 to 2 is 0.
@ Scythian: They cancelled school on account of ice :)
