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JEE Advanced Mathematics question

MathematicsDefinite IntegrationJEE Advanced

If , then equals

Answer: (B)

Solution

We are given

af(x)+bf(1/x)=Missing argument for \frac\frac1x-5 (1)

Replace by :

af(1/x)+bf(x)=x-5 (2)

Multiply (1) by and (2) by , then subtract to eliminate :

-=a(Missing argument for \frac\frac1x-5)-b(x-5)=Missing argument for \frac\frac ax-bx-5a+5b .

Integrate from 1 to 2:

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Question ID VK-109491