Ws 6.6 Improper Integrals Worksheet Page 2

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Calculus Maximus
WS 6.6: Improper Integrals
1
p  , what can be said in general about improper integrals of the form
3. If
converges for
dx
1
p
x
1
1
dx
? For what values of a does the function diverge? Converge? To what ?
p
a
x
4. Determine if the improper integral converges or diverges by finding a function to compare it to. Justify
by showing the inequality and discussing the convergence/divergence of the function to which you
compare.
3
5
x
x
1
dx
3 sin x
(a)
dx
(b)
dx
(c)
(d)
dx
6
4
2
5
2
2
1
4
x
x
1
(
x
4
x
1)
(
x
5)
Multiple Choice
3
2
x
5.
x e
dx
=
0
1
1
(A)
(B) 0
(C)
(D) 1
(E) Diverges
3
3
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