Homework 5
1)
a. 0.627805
b. 0.620609
c. 0.044256
d. 0.044935
e. 0.620609
2)
A) a. 3.058629
b. 4.978098
c. 8.034739
B) The approximations will be less than the actual value because the function is
increasing on the given interval and the function uses a left hand approximation. The errors
resulting from beginning with the left hand endpoint will cause the approximation to be less than
the integral’s actual value.
C) The values are different because of the discrepancy in the number of
rectangles/intervals used. The sum of the two integrals has a 1000 intervals in each term while
the single interval only has 1000. So the values will not be the same as a result of the difference
in error in both expressions.
D) To eliminate the difference mentioned in part C one would have to adjust the number
of intervals used in the second term (overall integral from 1 to 3) to 2000. Thus both expressions
would contain the same degree of accuracy and result in the same output.
3)
A) 8.042693
B) The actual value is less than the right hand rule approximation. This happens because