6thnx sir
i got it!!!:D
If a funcn. f(x) is bijective in [a,b] , then prove that integral a to b f(x) dx + integral f(a) to f(b) inverse of f(x) dx = b f(b) - a f(a)
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3 Answers
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The dotted region below gives integral of f(x)
while the dotted region to the left gives the integral of f-1x
Hence the proof...
This is a hint to your question (infact the complete solution..)
But I want some student to pick up the clue and give the complete clear proof :)
6another quesn...
For any real t , x = 1/2 ( et + e-t ) , y = 1/2 ( et - e-t) is a pt. on the hyperbola x2 - y2 = 1. Show that the area bounded by the hyperbola and the line joinin its center to the pts. corresponding to t1 and -t1 is t1.