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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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