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If f(a+b - x) = f(x) , then int(a)^(b)...

If ` f(a+b - x) = f(x) ,` then ` int_(a)^(b) x f(x) dx` is equal to

A

`(a+b)/(2)int_(a)^(b)f(b-x)dx`

B

`(a+b)/(2)int_(a)^(b)f(b+x)dx`

C

`(b-a)/(2)int_(a)^(b)f(x)dx`

D

`(a+b)/(2)int_(a)^(b)f(x)dx`

Text Solution

Verified by Experts

The correct Answer is:
D
Let ` l = int _(a)^(b) x f(x) dx " "` …(i)
Then , by a property of definite integrals
` l = int _(a)^(b) (a+b- x) f(a+b-x)dx" "`…(ii)
[ ` :' " Given" f(a+b-x) = f(x)]`
On adding Eqs. (i) and (ii) , we get
` 2l = int _(a)^(b) (a+b) f(x) dx rArr l = (a+b)/2 int _(a)^(b) f(x) dx `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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