Express the integrand as a sum of partial fractions and evaluate the integral.
-$$\int _ { 5 } ^ { 9 } \frac { 6 } { x ^ { 2 } - 9 } d x$$
A) -0.693
B) 2.773
C) 3.693
D) 0.693

Question

Quizplus · Accepted Answer

The given integral can be expressed as a sum of partial fractions by factoring the denominator $x^2 - 9$ as $(x - 3)(x + 3)$. Thus, we can write $\frac{6}{x^2 - 9}$ as $\frac{A}{x - 3} + \frac{B}{x + 3}$. Solving for A and B, we find that $A = \frac{3}{2}$ and $B = -\frac{3}{2}$. Therefore, the integral becomes $\int_{5}^{9} \left(\frac{3}{2(x - 3)} - \frac{3}{2(x + 3)}\right) dx$. Evaluating this integral gives a result of $0.693$.

Express the Integrand as a Sum of Partial Fractions and Evaluate