Question

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

• A. 0
• B. 1
• C. $2 \log _ { e } 3$
• D. None of these

Answer 1

Answer: (A)

0

Answer 2

Obviously the function $\frac { x ^ { 2 } \sin 2 x } { x ^ { 2 } + 1 }$is odd, so

$\int _ { - 3 } ^ { 3 } \frac { x ^ { 2 } \sin 2 x } { x ^ { 2 } + 1 } d x = 0$.