A) \[[a]f(a)-\{f(1)+f(2)+....+f([a])\}\]
B) \[[a]f([a])-\{f(1)+f(2)+....+f(a)\}\]
C) \[af([a])-\{f(1)+f(2)+....+f(a)\}\]
D) \[af(a)-\{f(1)+f(2)+....+f([a])\}\]
Correct Answer: A
Solution :
Since, \[\int_{1}^{a}{[x]f'}(x)dx=\int_{1}^{2}{f'}(x)dx\] \[+\int_{2}^{3}{2f'(x)+......+\int_{[a]}^{a}{[a]f'(x)dx}}\] \[=[f(x)]_{1}^{2}+2[f(x)]_{2}^{3}+.....+[a][f(x)]_{[a]}^{a}\] \[=[a]f(a)-\{f(1)+f(2)+....+f([a])\}\]
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