5. the function is continuous on the interval [10, 20] with some of its values given in the table above. estimate the average value of the function with a right hand sum approximation, using the intervals between those given points. (4 points)
x 10 12 15 19 20
f(x) -2 -5 -9 -12 -16

a -9.250
b -10.100
c-7.550
d-6.700

The average value of over the given interval is



You're given five points, but only four will contribute to the sum as there are four subintervals that you can work with. Because you are finding the right-endpoint approximation, the height of the rectangles used in the Riemann sum will be determined by the points , where the height of each rectangle is the corresponding value of and the width is the length of the subinterval. In this case, the lengths would be (left to right and respectively) , which is simply the set of forward differences of the previous set.

So the average value is approximated by

Yes, two vertical lines can be complementary