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if g(x) is the inverse of f(x) and f(x) has domain x belongs (1,5) closed,where f(1)=2and f(5)=10 then find the value of ∫f(x)dx limit is from 1 to 5 +∫g(y)dy limit is from 2 to 10

  1. if g(x) is the inverse of f(x) and f(x) has domain x belongs (1,5) closed,where f(1)=2and f(5)=10 then find the value of ∫f(x)dx limit is from 1 to 5 +∫g(y)dy limit is from 2 to 10
 
 
 

Grade:12th pass

1 Answers

Vikas TU
14149 Points
3 years ago
Dear Student,
As we reaize that g(x) is the inverse function of f(x) .
We have takesn the values of f(x) and g(x) as horizontal and verical sides of the graph.
 So, here the sum of the two limited integral reffered in the qstn will be-
 
 THE AREA of the big rectangle – the area of the smaller one
= 10x5 – 2x 1
= 48
So, The ans will be 48.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)
 

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