If dy/dx=1/x, then the average rate of change of y with respect to x on the closed interval [1, 4] is

a) -1/4
b) (1/2)*ln(2)
c) (2/3)*ln(2)
d) 2/5
e) 2

Answer: C

Question

If dy/dx=1/x, then the average rate of change of y with respect to x on the closed interval [1, 4] is 

a) -1/4
b) (1/2)*ln(2)
c) (2/3)*ln(2)
d) 2/5
e) 2

Answer: C

anonymous · Answer

@eliassaab @thomaster @ganeshie8

anonymous · Answer

@whpalmer4 @AravindG

anonymous · Answer

@kirbykirby @dumbcow

anonymous · Answer

if $\frac{dy}{dx}=\frac{1}{x}$ then $y=\ln(x)+c$

anonymous · Answer

$$\frac{\ln(4)-\ln(1)}{4-1}=\frac{\ln(4)-0}{3}=\frac{\ln(4)}{3}$$

anonymous · Answer

Thank you everyone!

anonymous · Answer

$$\frac{dy}{dx}=\frac{1}{x}$$

$$dy=\frac{1}{x}dx$$

$$\int dy=\int\frac{1}{x}dx$$
$$\int\limits_{0}^{y}dy=\int\limits_{1}^{4}\frac{1}{x}dx$$
$$y=ln(x)|_1^4$$
$$y=ln(4)-ln(1)$$
$$y=ln(2^2)-0$$
$$\boxed{\boxed{y=2ln(2)}}$$

anonymous · Answer

Thank you for the help!