Definite Integration Question 21

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

Options:

A) 0

B) 1

C) $ 2{\log _{e}}3 $

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

Obviously the function $ \frac{x^{2}\sin 2x}{x^{2}+1} $ is odd, so $ \int _{-3}^{3}{\frac{x^{2}\sin 2x}{x^{2}+1}}dx=0 $ .