Definite Integration Question 131
Question: $ \int _{-1}^{0}{\frac{dx}{x^{2}+2x+2}=} $
[MP PET 2000]
Options:
A) 0
B) $ \pi /4 $
C) $ \pi /2 $
D) $ -\pi /4 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int _{-1}^{0}{\frac{dx}{x^{2}+2x+2}} $
$ =\int _{-1}^{0}{\frac{dx}{{{(x+1)}^{2}}+1}} $
$ =[{{\tan }^{-1}}(x+1)] _{-1}^{0} $
$ =[{{\tan }^{-1}}1-{{\tan }^{-1}}0]=\frac{\pi }{4} $ .
BETA
