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Let f(x) be monotonically strictly increasing function in [3,5] such that ₃^5 f^2(x) d x=9 ; f(1)=3 ; f(4)=5 . Find the value of 2 ₁^4 x (5-f⁻¹(x) ) d x

Correct answer

7

Step-by-step solution

aligned ₁^4 x (5-f⁻¹(x) ) d x & = ₃^5 g(y)(5-y) g^ (y) d y= ((5-y) g^2(y) 2 )₃^5+ ₃^5 g^2(y) 2 d y -2 g^2(3) 2 + 9 2 & = 7 2 aligned Hence 2 ₁^4 x (5-f⁻¹(x) ) d x=7

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