Paragraph: Given that for each a ∈ ( 0 , 1 ) , lim h → 0 + ∫ h 1 − h t − a ( 1 − t ) a − 1 d t exists. Let this limit be g ( a ) . In addition, it is given that the function g ( a ) is differentia

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Paragraph: Given that for each a ∈ ( 0 , 1 ) , lim h → 0 + ​ ∫ h 1 − h ​ t − a ( 1 − t ) a − 1 d t exists. Let this limit be g ( a ) . In addition, it is given that the function g ( a ) is differentiable on ( 0 , 1 ) . Question: The value of g ′ ( 2 1 ​ ) is

TestHub · Accepted Answer

We have g a = g 1 - a and g is differentiable. ∴ g ' a = - g ' 1 - a Hence g ′ 1 2 = 0 .

Mathematics - Definite Integration Question with Solution | TestHub

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