Find the value of the integral $\int _ { 4 - \sqrt { 3 } } ^ { 4 + \sqrt { 3 } } \frac { 1 } { x ^ { 2 } - 8 x + 17 } d x$
A) $\frac { \pi } { 4 }$

B) $\frac { 4 \pi } { 3 }$
C) $\frac { \pi } { 10 }$
D) $\frac { 2 } { 3 }$
E) $\frac { \pi } { 3 }$
F) $\frac { 2 \pi } { 3 }$

G) $\frac { \pi } { 2 }$

H) $\frac { 1 } { 2 }$

Question

Find the value of the integral $\int _ { 4 - \sqrt { 3 } } ^ { 4 + \sqrt { 3 } } \frac { 1 } { x ^ { 2 } - 8 x + 17 } d x$ 
A) $\frac { \pi } { 4 }$ 
 
B) $\frac { 4 \pi } { 3 }$ 
C) $\frac { \pi } { 10 }$ 
D) $\frac { 2 } { 3 }$ 
E) $\frac { \pi } { 3 }$
F) $\frac { 2 \pi } { 3 }$

G) $\frac { \pi } { 2 }$

H) $\frac { 1 } { 2 }$

Quizplus · Accepted Answer

The integral can be evaluated using the method of residues. The integrand has two poles, at $x = 4 \pm \sqrt{3}$. The residue at $x = 4 + \sqrt{3}$ is $\frac{1}{2\sqrt{3}}$, and the residue at $x = 4 - \sqrt{3}$ is $\frac{1}{2\sqrt{3}}$. Therefore, the value of the integral is $\frac{2\pi}{3}$.

Find the Value of the Integral ∫4−34+31x2−8x+17dx\int _ { 4 - \sqrt { 3 } } ^ { 4 + \sqrt { 3 } } \frac { 1 } { x ^ { 2 } - 8 x + 17 } d x∫4−3​4+3​​x2−8x+171​dx

Find the Value of the Integral $\int _ { 4 - \sqrt { 3 } } ^ { 4 + \sqrt { 3 } } \frac { 1 } { x ^ { 2 } - 8 x + 17 } d x$