Question

For a function f(x) , Find the area enclosed by the inverse of f(x) , the x-axis and ordinate at x=2/3 .

Answer 1

\[f(x)=4x^3/3(1+x^2)\]

Answer 2

you may use integration by parts

Answer 3

I am not able to find the inverse directly .

Answer 4

The function f(x) and its inverse are symmetric about the line y=x . How do I use this information here ?

Answer 5

draw it out, you will see clearly