MH1627, Test 1
Name.
1. Using integration by parts, compute the given integrals:
.2 X
(a) fx 2 e 2x dx =
4105+ C
e
4,en zx  )iy x a)
(b) f(lnx) 2 dx =
44 ror
e all
Un (soy i eee
2. Compute the given trigonometric integrals:
(a)
V/(
3)

sin 2 x c
47Th,
,
15/
MH1627, Test 2
Name: P4(.
.kbl/rn
t
the graphs of y = x 2 and y = x + 2 and find its area.
X (.; 144 ete prfor ipt work)
1. Sketch the region bound
ay6
(7/2. Find the average value 'bf tl fuTion y = x sin x 2 over he interval [0, Fr/21.
Name:
PA /flip 710.4 A5
1. Compute the 9th partial sum of the given series:
0.
v(a)
9
1
= 1 1,
(Hint:
n(n + 1)
62
00
E c) (Hint: 2 1 = 1024).
Ti
511
n=1 `'
I 4.
In each of the following problems, determine whether the given series is convergent or
d
Name.
MH1627 Test 4.
1. Express the given function as a power series and find its interval of convergence:
Va)
f (x) =
xels
cA
.X3
f (x) =
2,
ln(1+ x )
XC
r. I
f=1)
(b)
+
coz
n
cl (1)
X
3
n4
)<
,th ( ( 4"
CI
k 3)
69 k
Approximate the numerical val
ANSWER KEY
old
Final Exam.
1. Evaluate the given integrals.
(a)
3x 1
f x2
x3
x
dx
dic
2
(b)
_1
=2
(c)
x
f_=
i
x;
(diver eat
in rat)
ipt 1,143a rrtanmC
7
2. Which of the given series converge and which diverge? (Indicate absolute or conditional
con
Test 2  Review guide (M1627 CALC II)
Problem 1 Evaluate the following integrals.
R
1) x1x+1 dx
2)
R1
(1 +
0
x)8 dx
Problem 2 Determine whether each integral is convergent or divergent. Evaluate
those that are convergent
R 1
R 1 2x
1) 1 (3x+1)
dx
2 dx, xe