NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice
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
Options
- A29
- B32
- C12
- D17
Correct answer
D. 17
Step-by-step solution
Since f x > 0   ∀ x ∈ 1,4 ⇒ f - 1 x > 0   ∀ x ∈ 3,8 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 ⇒ A 2 = 17 sq. units