Definite Integration Question 123
Question: The value of $ \int _{-a}^{a}{\frac{1}{x+x^{3}}dx} $ is
[AMU 2005]
Options:
A) 0
B) $ \int_0^{a}{\frac{1}{1+x^{6}}\ }dx $
C) $ 2\int_0^{a}{\frac{1}{1+x^{3}}\ }dx $
D) $ \int_0^{a}{\frac{1}{1+{{(a-x)}^{3}}}\ }dx $
Show Answer
Answer:
Correct Answer: A
Solution:
Since $ \int _{-a}^{a}{f(x)}\ dx=0 $ ,if $ f(-x)=-f(x) $
Therefore, $ \int _{-a}^{a}{\frac{dx}{x+x^{3}}}=0 $ .
BETA
