1. Tardigrade
  2. Question
  3. Mathematics
  4. The area bounded by y=f(x), x=1, x=4 and the x -axis is 12 square units where f(x) is a differentiable function such that f(1)=3 and f(4)=8. If f(x) is a bijective function which is always positive, then the area (in square units) bounded by y=f- 1(x), x=3, x=8 and the x -axis is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The area bounded by $y=f\left(x\right), \, x=1, \, x=4$ and the $x$ -axis is $12$ square units where $f\left(x\right)$ is a differentiable function such that $f\left(1\right)=3$ and $f\left(4\right)=8.$ If $f\left(x\right)$ is a bijective function which is always positive, then the area (in square units) bounded by $y=f^{- 1}\left(x\right), \, x=3, \, x=8$ and the $x$ -axis is equal to

NTA AbhyasNTA Abhyas 2020Application of Integrals

Solution:

Since $f\left(x\right)>0\forall x\in \left[1,4\right]$
$\Rightarrow f^{- 1}\left(x\right)>0\forall x\in \left[3,8\right]$
Solution
Note that the shaded area is the required area and $A_{1}=12.$
Let the required area be $A_{2}$
Also, $A_{1}+A_{2}=32-3=29$
$\Rightarrow A_{2}=17$ sq. units