Use the Sixth-Degree Taylor Polynomial Centered at Zero for the Function

Multiple Choice

Use the sixth-degree Taylor polynomial centered at zero for the function $f ( x ) = \frac { 1 } { \sqrt { 1 + x ^ { 2 } } }$ to approximate the integral $\int _ { 0 } ^ { 2 / 3 } \frac { 1 } { \sqrt { 1 + x ^ { 2 } } }$ . Round your answer to nearest ten thousandth.

A) 0.6222
B) 0.6322
C) 0.8772
D) 0.6272
E) 0.3772