Integral Calculus Question 370
Question: $ \int_{{}}^{{}}{e^{x}[ {{\sin }^{-1}}\frac{x}{a}+\frac{1}{\sqrt{a^{2}-x^{2}}} ]dx=} $
Options:
A) $ \frac{1}{a}e^{x}{{\sin }^{-1}}\frac{x}{a}+c $
B) $ ae^{x}{{\sin }^{-1}}\frac{x}{a}+c $
C) $ e^{x}{{\sin }^{-1}}\frac{x}{a}+c $
D) $ \frac{e^{x}}{\sqrt{a^{2}-x^{2}}}+c $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_{{}}^{{}}{e^{x}[ {{\sin }^{-1}}\frac{x}{a}+\frac{1}{\sqrt{a^{2}-x^{2}}} ]},dx $ $ =\int_{{}}^{{}}{e^{x}{{\sin }^{-1}}\frac{x}{a},dx}+\int_{{}}^{{}}{\frac{e^{x}}{\sqrt{a^{2}-x^{2}}}},dx $ $ =e^{x}{{\sin }^{-1}}\frac{x}{a}-\int_{{}}^{{}}{\frac{e^{x}}{\sqrt{a^{2}-x^{2}}}},dx+\int_{{}}^{{}}{\frac{e^{x}}{\sqrt{a^{2}-x^{2}}}},dx+c $ $ =e^{x}{{\sin }^{-1}}\frac{x}{a}+c. $
BETA
