Integral Calculus Question 113
Question: $ \int_{{}}^{{}}{{e^{-x}}cose{c^{2}}(2{e^{-x}}+5)}\ dx= $
[AISSE 1988]
Options:
A) $ \frac{1}{2}\cot (2{e^{-x}}+5)+c $
B) $ -\frac{1}{2}\cot (2{e^{-x}}+5)+c $
C) $ 2\cot (2{e^{-x}}+5)+c $
D) $ -2\cot (2{e^{-x}}+5)+c $
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ 2{e^{-x}}+5=t\Rightarrow -2{e^{-x}}dx=dt, $ then $ \int_{{}}^{{}}{{e^{-x}}cose{c^{2}}(2{e^{-x}}+5),dx}=-\frac{1}{2}\int_{{}}^{{}}{cose{c^{2}}t,dt} $ $ =\frac{1}{2}\cot t=\frac{1}{2}\cot (2{e^{-x}}+5)+c $ .
BETA
