A) \[k=100,m=1\]
B) \[k=99,m=\frac{1}{2}\]
C) \[k=99,m=1\]
D) \[k=100,m=-\frac{1}{2}\]
Correct Answer: D
Solution :
\[I=\int_{{}}^{{}}{{{e}^{x}}}\left( \sqrt{\frac{1+{{x}^{100}}}{1-{{x}^{100}}}}+\frac{100{{x}^{99}}}{(1-{{x}^{100}})\sqrt{1-{{x}^{200}}}} \right)dx\] Now\[\frac{d}{dx}\left( \sqrt{\frac{1+{{x}^{100}}}{1-{{x}^{100}}}} \right)=\frac{100{{x}^{99}}}{\left( 1-{{x}^{100}} \right)\sqrt{1-{{x}^{200}}}}\] Use\[I=\int_{{}}^{{}}{{{e}^{x}}(f(x)+f(x))={{e}^{x}}f(x)+C}\]You need to login to perform this action.
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