If f ( x ) is continuous function and F ( x ) = ∫ 0 x ( ( 2 t + 3 ) ⋅ ∫ t 2 f ( y ) d y ) d t , Then ∣ F ′′ ( 2 ) / f ( 2 ) ∣ is

Question

If f ( x ) is continuous function and F ( x ) = ∫ 0 x ​ ( ( 2 t + 3 ) ⋅ ∫ t 2 ​ f ( y ) d y ) d t , Then ∣ F ′′ ( 2 ) / f ( 2 ) ∣ is

TestHub · Accepted Answer

(1) F ′ ( x ) = ( 2 x + 3 ) ∫ x 2 ​ f ( x ) d x 2 x + 3 F ′ ( x ) ​ = ∫ x 2 ​ f ( x ) d x ( 2 x + 3 ) 2 ( 2 x + 3 ) F ′′ ( x ) − 2 F ′ ( x ) ​ = − f ( x ) . ⇒ ​ f ( 2 ) F ′′ ( 2 ) ​ ​ = 7 Ans

Mathematics - Definite Integration Question with Solution | TestHub

Doubts & Discussion

JEE Advanced (2028)