6.1#1
What's the integral? A total of 8 1/2 squares. So the average is 8.5/5 = 1.7.
#10
a) Plug in t=0 and t=6, since t is in months from the beginning. We get
100 at the beginning, and 100 e^-3 or about 5 at the end.
b) The int(100 e^-.5t), t from 0 to 6, is 100*(e^-3 - 1)/(-.5) or about 190.
Dividing that by the 6 months, we get about 32.
#12.
a) Plug in t=10,20; get about 2.66 and 1.76.
b) The average of those two numbers is about 2.21.
c) For this we need to integrate Q from 10 to 20, and divide by 10.
That integral is just an exponential and we get 21.8, or dividing by 10,
an average of 2.18.
d) The second is slightly lower because the exponential is not just
a straight line between 10 and 20; it's slightly concave up.
#15
a) The average is least over [0,5] - even slightly negative. (The others
are all positive.)
b) The average is greatest over [0,1]. The other intervals just bring in
new numbers that are less than the value at 1.
c) Since it's symmetric, from [0,2] gets the same as [-2,2].
#16
(c) is negative, (b) looks about 0, and (a) is positive, so (c) < (b) < (a).