Definite Integration Question 478

Question: $ \int _{-3}^{3}{\frac{x^{2}\sin x}{1+x^{6}}dx=} $

Options:

A) 4

B) 2

C) 0

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

$ \int _{-3}^{3}{\frac{x^{2}\sin x}{1+x^{6}}}dx=0 $ . By the property of definite integral, $ \int _{-a}^{a}{f(x)dx=0} $ , when $ f(x)=-f(-x) $ .