Let f (x) be a conitnuous function defin...

Let f (x) be a conitnuous function defined on [0,a] such that `f(a-x)=f(x)"for all" x in [ 0,a]`. If ` int_(0)^(a//2) f(x) dx=alpha,` then `int _(0)^(a) f(x) dx` is equal to

A

`alpha`

B

`2 alpha`

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

B

We have,
` underset(0)overset(a)int f(x) d=underset(0)overset(a//2)int [f(x) +f(a-x)] dx=underset(0)overset(a//2)int 2f (x)dx=2 alpha`

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