A) 3
B) 2
C) 1
D) 0
Correct Answer: A
Solution :
[a] We have \[I=\int\limits_{4}^{10}{\frac{[{{x}^{2}}]dx}{[(14-{{x}^{2}})]+[{{x}^{2}}]dx}}\] by using property \[\int\limits_{a}^{b}{f(x)dx}=\int\limits_{a}^{b}{f(a+b-x)dx}\] Also, \[I=\int\limits_{4}^{10}{\frac{[(4+10-{{x}^{2}})dx]}{[{{(14-(14-x))}^{2}}]+[{{(14-x)}^{2}}]}}\] \[2I=\int\limits_{4}^{10}{\left( \frac{[{{x}^{2}}]}{[{{(14-x)}^{2}}]+{{[x]}^{2}}}+\frac{[{{(14-x)}^{2}}]}{{{[x]}^{2}}+[{{(14-x)}^{2}}]} \right)dx}\] \[=\int\limits_{4}^{10}{1.dx\Rightarrow I=3}\]
You need to login to perform this action.
You will be redirected in
3 sec
