Mathematics

Integrate $$\displaystyle \overset { 7 }{ \underset { 4 }{ \int }  } \dfrac{(11 - x)^2}{x^2 + ( 11 - x)^2} dx$$


SOLUTION
$$I=\int^7_4{\cfrac{(11-x)^2}{x^2+(11-x)^2}}dx\rightarrow(1)\\ \quad=\cfrac{(11-(11-x))^2}{(11-x)^2+(11-(11-x))^2}dx\\I=\int^7_4\cfrac{x^2dx}{(11-x)^2+x^2}\rightarrow(ii)$$
$$(i)+(ii)\Rightarrow 2I=\int^7_4dx=3\\ \Rightarrow I=3/2$$
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Subjective Medium Published on 17th 09, 2020
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