Find the value of the integral $\int _ { - 3 } ^ { 3 } \frac { x } { \sqrt { 1 + 3 x ^ { 2 } } } d x$
A) $\frac { 2 } { 3 } ( \sqrt { 7 } - 1 )$

B) $\sqrt { 7 } - 1$
C)0
D) $\frac { 1 } { 3 }$
E)$\frac { 2 } { 3 }$
F) $\frac { 1 } { \sqrt { 7 } }$
G) $\sqrt { 7 }$
H)Does not exist

Question

Find the value of the integral $\int _ { - 3 } ^ { 3 } \frac { x } { \sqrt { 1 + 3 x ^ { 2 } } } d x$ 
A) $\frac { 2 } { 3 } ( \sqrt { 7 } - 1 )$ 
 
B) $\sqrt { 7 } - 1$ 
C)0
D) $\frac { 1 } { 3 }$ 
E)$\frac { 2 } { 3 }$
F) $\frac { 1 } { \sqrt { 7 } }$ 
G) $\sqrt { 7 }$ 
H)Does not exist

Quizplus · Accepted Answer

The function $f(x) = \frac{x}{\sqrt{1+3x^2}}$ is an odd function because $f(-x) = -f(x)$. The integral of an odd function over a symmetric interval $[-a, a]$ is always 0.

Find the Value of the Integral ∫−33x1+3x2dx\int _ { - 3 } ^ { 3 } \frac { x } { \sqrt { 1 + 3 x ^ { 2 } } } d x∫−33​1+3x2​x​dx

Find the Value of the Integral $\int _ { - 3 } ^ { 3 } \frac { x } { \sqrt { 1 + 3 x ^ { 2 } } } d x$