See graph of 2 functions, √(1 - (x -1)² and x√(1 - (x -1)² http://i254.photobucket.com/albums/hh120/Scythian1950/CalculusProblem120913_zps95856e68.jpg Prove that they have the same area. Maybe you can do this without calculus?

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 :)

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Scythian1950

Lv 7

Scythian1950 a posé la question dans Science & Mathematics Mathematics · il y a 7 ans

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?

Mise à jour:

√(1 - (x -1)²) and x√(1 - (x -1)²), that is. A semicircle and a bent semicircle.

Mise à jour 2:

Having an easy time, Quadrilerator?

1 réponse

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Quadrillerator
Lv 5
il y a 7 ans
Réponse favorite
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 :)

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