Answer:
Average velocity of the function over the given interval
= [tex]log(\frac{7}{4} ) -2[/tex]
Step-by-step explanation:
Explanation:-
Given function y = 3/x -2 ...(i)
The average velocity of the function over the given interval
Average velocity = [tex]\frac{1}{b-a} \int\limits^b_a {(\frac{3}{x} -2)} \, dx[/tex]
= [tex]\frac{1}{7-4} \int\limits^7_4 {(\frac{3}{x} -2)} \, dx[/tex]
now integrating
= [tex]\frac{1}{3}( \int\limits^7_4 {(\frac{3}{x} )} \, dx-2\int\limits^7_4 {1} \, dx )[/tex]
= [tex]\frac{1}{3} (3 (log x) - 2 x )_{4} ^{7}[/tex]
= [tex]\frac{1}{3}( (3 (log 7) - 14 )-(3 log 4 -8))[/tex]
by using formulas
log a-log b = log(a/b)
on simplification , we get
= [tex]\frac{1}{3}( (3 (log 7) -3 log 4 ) - \frac{1}{3} (6)[/tex]
= [tex]log(\frac{7}{4} ) -2[/tex]
Average velocity of the function over the given interval
= [tex]log(\frac{7}{4} ) -2[/tex]
