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Calculus II Quiz
#2 February
25, 2005
Name____________________ R. Hammack Score
______
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(1) Find
the following definite integrals. Use either the Fundamental Theorem of Calculus
or the various properties of definite integrals, whichever is most applicable.
Write your final answer in the simplest possible form.
(a) 5dx= -5dx=-5π
=
-
(Using the fact that the graph of y=
is a semicircle of radius 1, centered at the origin.
(b)
dx=
=ln(e)-ln(1/e)=ln(e)+ln(e)=2
(c)
(-x+4)dx=
=-+4=
(2) Consider
the function F(x)=(+2t-15)dt
(a) F '(x)=
(+2x-15)
(b) At which x
values (if any) is the tangent to the graph of y=F(x)
horizontal?
F '(x)=(+2x-15)=(x-3)(x+5)
Derivative is 0 when x
= 3 or x
= -5, so that's where the tangent to F
is horizontal.