A) 3
B) 7
C) 6
D) \[\frac{1}{3}\]
Correct Answer: A
Solution :
\[I=\int\limits_{4}^{10}{\frac{[{{x}^{2}}]}{[{{x}^{2}}-28x+196]+[{{x}^{2}}]}}\] ??....(i) Use property\[\int\limits_{a}^{b}{f(a+b-x)dx=\int\limits_{a}^{b}{f(x)dx}}\] \[\Rightarrow \,I=\int\limits_{4}^{10}{\frac{[{{x}^{2}}-28x+196]dx}{[{{x}^{2}}]+[{{x}^{2}}-28x+196]}}\]4 .......... (ii) by (i) and (ii) \[2I=\int\limits_{4}^{10}{dx=10-4=6}\] I = 3
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