Math 121 Calculus II Spring 2006
Prob Pts
1
2
3
4
5
6
7
8
9
Total
Final Exam Name: (print neatly)
Instructor: (sign)
1. (24 pts.) Evaluate the following derivatives.
a) d
dxe1−x2=
b) d
dx ³ln(x√ex) + ln(x√e)´=
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Material Type: Exam; Class: CALCULUS II; Subject: Mathematics; University: Clark University; Term: Spring 2006;
Typology: Exams
Pre 2010
1 / 10
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Prob Pts Math 121^ Calculus II^ Spring 2006
Total
Final Exam Name: (print neatly)
Instructor: (sign)
- (24 pts.) Evaluate the following derivatives.
a)
d
dx
e
1 −x^2
b)
d
dx
( ln(x
ex) + ln(x
e)
)
c)
d
dx
x
3 x
d)
d
dx
arctan(x
2 ) =
c)
∫ x + 1
ex^
dx
d)
∫
ln(x
3 − x) dx
e)
∫
πx^ dx
f)
∫ 1 + x
1 + x^2
dx
- (12 pts.) Find the area between the curves y =
x and y =
x
5
Find the area of the region
√√√√√√√√√√√√√√√√√√√√√√ -
6
x
- (12 pts.) Find the volume of the solid obtained by rotating the region between the
curves y =
x and y =
x
5
about the axis y = 5.
√√√√√√√√√√√√√√√√√√√√√√ -
6
x
- (10 pts.) Use integration by parts to evaluate the following.
a)
∫
xe
1 −x dx.
b)
∫
(x
3 − x + 1) ln(x + 1) dx.