
% Section 8.8: % Improper integrals
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Section 8.8: 
Problems: 35, 39, 41, 45, 55, 65, 66.%, 77, 81, 83.
% Problems: 7, 13, 19, 21, 25, 31, 35, 39, 42, 45, 46, 55, 65, 66, 77, 81, 83.
% problem 77 is harder,need more hint
% Hint for problem 77:

% Section 8.8: % Improper integrals
\item
Section 8.8: 

Let $f(x) = \ds{1 \over x^{0.5} \ln x}$.
Is the improper integral $\ds{\int_{e}^\infty f(x) \ dx}$ convergent?

Hint: Try not to find the anti-derivative of $f(x)$, but instead find a suitable $g(x)$
for comparison using Theorem 2 or Theorem 3.
See also Example 5-7 of Lecture 02 on how to find $g(x)$.

% Section 8.8: % Improper integrals
\item
Section 8.8: 

Do the same for $\ds{\int_0^{1\over e} \ds{1 \over x^2 |\ln x|} \ dx}$.

