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Question
`int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"("k" - "x") "dx"`, then the value of k is:
Options
a
2a
Independent of a
None of the above options
Solution
2a
Explanation:
Given, `int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"("k" - "x") "dx"` ...........(i)
We know, from properties of integrals
`int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"(2"a" - "x") "dx"` ..........(ii)
From equations (i) and (ii), we get
k = 2a
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