242 Math Homework 6
Sections 012 and 014: Due Wednesday March 23rd
Section 050: Due Tuesday March 22nd
Questions 1 through 5 should be done by hand.
For questions 6 through 8, you can use Maple as much or as little as you like.
1. Evaluate
sin(ln x) dx. (May be a little tricky.)
2. Evaluate
x2
0
x
dx or show that it is divergent.
+2
3. Use Newtons Method to nd a good approximation to 99991/4 .
4. Find the length of the curve = y ln(sec x) between x = 0 and x = /4.
5. Find the length of the curve y = ln(1 x2 ) between x = 0 and x = 1/2.
5
cos x
dx using both the Trapezoid Rule and Simpsons Rule
x
1
with n = 8, n = 16, and n = 32.
6. Estimate
1
7. Estimate
2
ex dx using both the Trapezoid Rule and Simpsons Rule
0
with n = 4 and n = 10.
8. Use Simpsons Rule with n = 10 to estimate the length of the curve
y = xex between x = 0 and x = 5.
1