Let f : R → R be a differentiable function having f ( 2 ) = 6 , f ′ ( 2 ) = ( 48 1 ) . Then lim x → 2 ∫ 6 f ( x ) x − 2 4 t 3 d t equals

Question

Let f : R → R be a differentiable function having f ( 2 ) = 6 , f ′ ( 2 ) = ( 48 1 ​ ) . Then lim x → 2 ​ ∫ 6 f ( x ) ​ x − 2 4 t 3 ​ d t equals

TestHub · Accepted Answer

x → 2 lim ​ ∫ 0 f ( x ) ​ x − 2 4 t 3 ​ d t Applying L Hospital rule ​ x → 2 lim ​ [ 4 f ( x ) 2 f ′ ( x ) ] = 4 f ( 2 ) 3 f ′ ( 2 ) = 4 × 6 3 × 48 1 ​ = 18. ​

Mathematics - Definite Integration Question with Solution | TestHub

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