Definite Integration Question 9
Question: The value of $ \int _{-1}^{1}{(\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}})dx} $ is
Options:
A) 0
B) 1
C) $ -1 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ f(x)=\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}} $ .
Then $ f(-x)=\sqrt{1-x+x^{2}}-\sqrt{1+x+x^{2}}=-f(x) $
Hence $ f(x) $ is an odd function and so $ \int _{-1}^{1}{f(x)dx=0} $ .
BETA
