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mi9lys1exysouzo
mi9lys1exysouzo mi9lys1exysouzo
  • 31-08-2016
  • Mathematics
Answered

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)
D2/5
E2

Verified Answer :

meerkat18
meerkat18 meerkat18
  • 02-09-2016

The first thing to do here is to integrate the ordinary differential equation dy/dx = 1/x. This is equal to  y = ln x + C. Assuming C is zero. y = lnx. substituting the two interval, 
y1 = 0 y2 = ln 4
the rate of change then is equal to (ln4 - 0) / (4-1) equal to 2/3 ln 2. Answer is C

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