99 Percentile Qs Bank for JEE MainMathematicsFunctions

If 2 f(x)-3 f ( 1 x )=x , then ₁^e f(x) d x=

Options

A- ( 2+ e ^2 5 )
B2+ e 5
C2+ e ^2 5
D2- e ^2 5

Correct answer

A. - ( 2+ e ^2 5 )

Step-by-step solution

2 f(x)-3 f ( 1 x )=x ...(1) and replacing x by 1 x , we get 2 f ( 1 x )-3 f(x)= 1 x [ 2 equation (1) ]+[3 equation (2) ] gives, aligned & 4 f(x)-9 f(x)=2 x+ 3 x -5 f(x)=2 x+ 3 x & f(x)= -2 5 x- 3 5 x aligned aligned & ₁^ e f ( x ) dx = ₁^ e ( -2 5 x - 3 5 x ) d x= -2 5 ₁^ e x d x - 3 5 ₁^ e 1 x dx & = -2 5 [ x ^2 2 ]₁^ e - 3 5 [ x ]₁^ e = -1 5 ( e ^2-1 )- 3 5 ( e - 1)= -1 5 e ^2+ 1 5 - 3 5 & =- ( 2+ e ^2 5 ) aligned

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