If f(a+b-x)=f(x) then \int_{a}^{b} x f(x) \dx is equal to [AIEEE 2003]

Correct Answer is : a+b2b∫af(x)dx

\frac{a+b}{2} \int_{a}^{b} f(a+b+x) \dx

\frac{a+b}{2} \int_{a}^{b} f(b-x) \dx

\frac{a+b}{2} \int_{a}^{b} f(x) \dx

\frac{b-a}{2} \int_{a}^{b} f(x) \dx

AIEEE 2003 Math Solved Paper

Section: Mathematics

Question : 36 of 66

Marks: +1, -0

If f(a+b−x)=f(x) then

∫

xf(x)‌dx is equal to

[AIEEE 2003]

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