Find . 1 2 3 4 5 0% 0% 0% 0% 0% dx x x ) 3 ( 2 c x x 2 3 1. c x x 2 3 2 3 2. c x x 2 2 3 3. c x 1 6 4. Don’t know 5.
Find. 1. 2. 3. 4. Don’t know 5.. Find. 1. 2. 3. 4. Don’t know 5.
Jan 14, 2016
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Find .
1 2 3 4 5
0% 0% 0%0%0%
dxxx )3( 2
cxx 231.
cxx 23
2
32.
cx
x 2
23
3.
cx 164.
Don’t know5.
Find .
1 2 3 4 5
0% 0% 0%0%0%
xdx3sin
cx
3cos3
11.
cx 3cos3
12.
x3cos3
13.
cx 3cos34.
Don’t know5.
Find .
1 2 3 4 5
0% 0% 0%0%0%
dxx4
1
cx
55
11.
cx
5
52.
cx
33
13.
cx
33
14.
Don’t know5.
Find .
1 2 3 4 5
0% 0% 0%0%0%
dxekx
cekx
kx 11.
cek
kx 12.
ckekx 3.
cekx 4.
Don’t know5.
Integrate .
1 2 3 4 5
0% 0% 0%0%0%
dxx 21
cx 2
1
2
11.
cx
23
3
22.
cx 21
2
3.
cx 21
2
14.
Don’t know5.
Integrate .
1 2 3 4 5
0% 0% 0%0%0%
dtt6
ct 23
4
1.
ct 32
2
32.
ct 23
3
23.
ct 23
9
4.
Don’t know5.
Tru
e
Fal
se
Don’t
know
0% 0%0%
dxxgdxxfdxxgxf )()()]()([
1. True
2. False
3. Don’t know
Tru
e
Fal
se
Don’t
know
0% 0%0%
b
a
a
b
dxxfdxxf )()(
1. True
2. False
3. Don’t know
Integrate .
1 2 3 4 5
0% 0% 0%0%0%
dxxx )sin3(
cxx 23
3
2cos3
1.
cxx 23
3
2cos3
2.
cxx )3
2cos3( 2
3
3.
cxx 23
2
3cos3
4.
None of these5.
Integrate .
1 2 3 4 5
0% 0% 0%0%0%
dtt 2)2(
ct 3)2(3
11.
cttt
423
23
2.
ct 3)2(33.
cttt
423
234.
Don’t know5.
Integrate .
1 2 3 4 5
0% 0% 0%0%0%
dttsinh
ct cosh1.
ct cosh2.
ct sinh3.
ct
cosh
14.
Don’t know5.
Find .
1 2 3 4 5
0% 0% 0%0%0%
3
0
3dxx
c4
811.
4
812.
93.
274.
Don’t know5.
Find .
0
cos xdx
Evaluate .2
1
dxex
Evaluate .
0
dxex
Calculate the area bounded by y=2x and the x-axis between x=2 and x=4.
Find the total area enclosed by the curve y=cosx and the x-axis between
x=0 and x=π.
Which is the correct formula for integration by parts for indefinite
integrals?
1 2 3 4
0% 0%0%0%
dxdx
duvuvdx
dx
dvu
1.
dxdx
dvuuvdx
dx
dvu
2.
dxdx
duvuvdx
dx
dvu
3.
dxdx
dvuuvdx
dx
dvu
4.
Integrate .
1 2 3 4 5
0% 0% 0%0%0%
xdxx sin)2(
xxx sincos)2( 1.
xxx sincos)2( 2.
xxx sincos)2( 3.
xxx sincos)2( 4.
None of these5.
Find .
1 2 3 4 5
0% 0% 0%0%0%
dxex x23
cexeex xxx 663 21.
cexeex xxx 663 22.
cexeex xxx 663 23.
cexeex xxx 663 24.
Don’t know5.
Evaluate .
0
cos xdxx
Evaluate .1
0
23 dxex x
Evaluate . 2
1
cos)4( xdxx
Use a suitable substitution to find
1 2 3 4 5
0% 0% 0%0%0%
.sincos2 xdxx
cx 3cos3
11.
cx 2cos2.
cx 3cos3
13.
cx 2cos2
14.
Don’t know5.
Use a suitable substitution to find
1 2 3 4 5
0% 0% 0%0%0%
.)7sin(4 43 dttt
ct )7cos( 41.
ct )7cos(4
1 4
2.
ct )7cos(4
1 4
3.
ct )7cos( 44.
Don’t know5.
Evaluate the integral by
making a suitable substitution.
dttt4
1
32 sin
Evaluate by making a suitable substitution.
dxx 6
1
8)23(
Which substitution would be most helpful to evaluate the integral
1 2 3 4
0% 0%0%0%
?23
dxxex
3xu 1.
2xu 2.
3xeu 3.
None of these4.
Which of the following is an incorrect step when finding the definite integrand
by the substitution method.
1 2 3 4 5
0% 0% 0%0%0%
6
0
21 dxxx
21 xu 1.
xdxdu
2
2.
6
02
1duu
3.
KnowtDon'
4.
None of the above5.
Find .
1 2 3 4 5
0% 0% 0%0%0%
dxxx
x
123
262
cxx
x
123
26ln
2
1.
cx
xx
26
123ln
2
2.
cxx 123ln 23.
cx 26ln4.
Don’t know5.
Evaluate .
1
02 1
dtt
t
Express in partial fractions.
1 2 3 4 5
0% 0% 0%0%0%
dxxx 2
2
dxxx
2
1
21.
dxxx
1
212.
dxxx
1
223.
dxxx
1
224.
Don’t know5.
Express in partial fractions.
1 2 3 4 5
0% 0% 0%0%0%
dxxx
x
253
142
dxxx
)2(7
9
)13(7
11.
dxxx
)2(9
7
13
72.
dxxx
)2(7
9
13
13.
dxxx
)2(7
1
)13(7
94.
Don’t know5.
Evaluate .dxxx
3
1 )5)(1(
1
Evaluate .dxxx
6
22
1
If a carrot has been chopped into n small pieces and the ith piece is Δxi
millimetres long, then the total length of
the string is .
Tru
e
Fal
se
Don’t
know
0% 0%0%
1. True
2. False
3. Don’t know
n
iix
1
If g is continuous on the interval
[m, n], then is a number.
Tru
e
Fal
se
Don’t
know
0% 0%0%
1. True
2. False
3. Don’t know
n
m
dttg )(
If the derivatives of f and g are the same then f=g.
Tru
e
Fal
se
Don’t
know
0% 0%0%
1. True
2. False
3. Don’t know
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