Question

Find the average velocity of the function over the given interval.

Answer 1

Answer:

Average velocity of the function over the given interval

              =  $log(\frac{7}{4} ) -2$

Step-by-step explanation:

Explanation:-

Given function y = 3/x -2 ...(i)

The average velocity of the function over the given interval

             Average velocity  = $\frac{1}{b-a} \int\limits^b_a {(\frac{3}{x} -2)} \, dx$

                               =    $\frac{1}{7-4} \int\limits^7_4 {(\frac{3}{x} -2)} \, dx$

now integrating

                           =   $\frac{1}{3}( \int\limits^7_4 {(\frac{3}{x} )} \, dx-2\int\limits^7_4 {1} \, dx )$

                           = $\frac{1}{3} (3 (log x) - 2 x )_{4} ^{7}$

                        =   $\frac{1}{3}( (3 (log 7) - 14 )-(3 log 4 -8))$

by using formulas

                 log a-log b = log(a/b)

  on simplification , we get                  

                 = $\frac{1}{3}( (3 (log 7) -3 log 4 ) - \frac{1}{3} (6)$

                = $log(\frac{7}{4} ) -2$

Average velocity of the function over the given interval

              =  $log(\frac{7}{4} ) -2$