Question

evaluate the definite integral below.
int_{8}^{11} \frac{6}{x} dx
enter your answer in exact form or rounded to two decimal places.

Explanation:

Step1: Recall integral formula

$\int\frac{1}{x}dx=\ln|x|+C$, so $\int\frac{6}{x}dx = 6\ln|x|+C$

Step2: Apply fundamental theorem

$6[\ln x]_8^{11}=6(\ln11 - \ln8)$

Step3: Simplify result

$6\ln\frac{11}{8}\approx6\times0.3283 = 1.97$

Answer:

$6\ln\frac{11}{8}\approx1.97$