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

Answer 1

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