If f( a + b +1- x )= f ( x ) , for all x, where a and b are fixed positive real numbers…
Mathematics · JEE Main · NTA Exams — Integral Calculus
If \(f(\mathbf{a}+\mathbf{b}+1-\mathbf{x})=\mathrm{f}(\mathbf{x})\), for all x, where a and b are fixed positive real numbers, then \(\frac{1}{(a+b)} \int_{a}^{b} x f(f(x)+f(x+1)) d x\) is equal to :
- \(\int_{a+1}^{b+1} f(x+1) d x\)
- \(\int_{n-1}^{b-1} f(x+1) d x\)
- \(\int_{i+1}^{i+1} f(x) d x\)
- \(\int_{n-1}^{b-1} f(x) d x\)
Answer
(D) _ n-1 ^ b-1 f(x) d x
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