Evaluate the integral.
-
A) -7
B) 12
C) 7
D) 2

Name: Evaluate the integral. - A) -7 B) 12 C) 7 D) 2
Brand: Quizplus
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Question

Evaluate the integral.
-
A) -7 
B) 12 
C) 7 
D) 2

Quizplus · Accepted Answer

Using the substitution method, let $u = x^2+6$. Then $du = 2xdx$. We can rewrite the integral as
\begin{align*}
\int_5^{11} \frac{x}{x^2+6}dx &= \frac{1}{2}\int_{11}^{47} \frac{1}{u} du \
&= \frac{1}{2} [\ln|u|]_{11}^{47} \
&= \frac{\ln|47| - \ln|11|}{2}\
&= \ln\sqrt{\frac{47}{11}}\
&\approx 2.
\end{align*}
Therefore, the best choice is (D) 2.

Evaluate the Integral. -