Integration Review Problems-Solution

For each of the following, pick the correct integ ration method to use in the first step of finding the antideriva -tive.

	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident
	IBP	long division	partial frac	subst	table	trig ident

Carefully de termine whether each of the fol lowing converges or not. If it converges, find its value . If it does
not, explain why.

	Diverges. Compare with (or a smaller multiple ).
	Converges.
	Diverges. Compare with
	Diverges.
	Converges.
	(hint: consider three cases.) Converges if p > 1 (work out three cases: p < 1, p = 1, and p > 1).

Please note! The problems on this review sheet are (probably) not like (or at least not exactly like) those
that will show up on the midterm. However, the skills that you need to do these are (probably) those you’ll
need to do well on the midterm.