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Calculus II Quiz
#1 February
14, 2005
Name____________________ R. Hammack Score
______
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(1) Find
the following antiderivatives.
(a) ∫(2+
+x+1)dx
=
+ln|x|+
+x+C
(b) ∫(
-
(x))dx
=
-tan(x)+C
(c) ∫sec(4x)tan(4x)
dx
= ∫sec(4x)tan(4x)
4dx
=
∫sec(u)tan(u)
4du=
sec(u)+C=
sec(4x)+C
u = 4x
du = 4dx
(d) ∫dx= ∫
cos(x)dx=∫
du=ln|u|+C=ln|5+sin(x)|+C
u = 5+sin(x)
du = cos(x)dx
(2) Find the
exact value of the following sums.
(a) (2+
)= (
2)+(
)=
(100·2)+(-
+
-
+
-
+
...-
+
)
= 200 + 0 = 200
(b) cos(2k
π)= cos(2 π)+cos(4 π)+cos(6 π)+...+cos(200 π)=1+1+1+...+1
= 100