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JEE Advanced Mathematics question

MathematicsDefinite IntegrationJEE Advanced

If then is equal to

Answer: (A),(C)

Solution

Use :

I= xf(x) dx=(a+b-x)f(a+b-x) dx=(a+b-x)f(x) dx=(a+b)f(x) dx-I .

So , giving . This is option **(a)**.

Checking the other options: - **(c)** is the same as (a), because

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Question ID VK-110092