Integral Calculus Question 374
Question: is equal to
[RPET 2000]
Options:
A) $ -e^{x}\tan ,( x/2 ) $
B) $ -e^{x}\cot ,( x/2 ) $
C) $ -\frac{1}{2}e^{x}\tan ,( \frac{x}{2} ) $
D) $ \frac{1}{2}e^{x}\cot ,( \frac{x}{2} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int{e^{x}( \frac{1-\sin x}{1-\cos x} )dx} $ $ =\int{e^{x}( \frac{1-\sin x}{2{{\sin }^{2}}(x/2)} ),dx} $
Þ $ I=\int{e^{x}( \frac{1}{2}cose{c^{2}}\frac{x}{2}-\cot \frac{x}{2} )},dx $ $ ( \because \int{e^{x}( f(x)+f’(x) )}=e^{x}f(x)+c ) $
$ \therefore I=e^{x}( -\cot \frac{x}{2} )+c=-e^{x}\cot \frac{x}{2}+c $ .
BETA
