Transcript Document

Find  (3x
2
 x)dx .
1.
x  x c
3
2
4.
6 x 1  c
2.
3 3
2
x  x c
2
5.
0%
0%
5
0%
4
0%
3
0%
2
2
x
3
x  c
2
Don’t know
1
3.
Find  sin 3xdx .
1.
1
cos 3x  c
3
4.
3 cos 3x  c
2.
1
cos 3 x  c
3
0%
0%
0%
5
0%
3
0%
2
1
cos 3 x
3
Don’t know
1
3.
4
5.
Find 
1.
1
c
5
5x
2.
5
c
5
x
1
dx .
4
x
4.
1
c
3
3x
0%
0%
0%
5
0%
3
0%
2
1
c
3
3x
Don’t know
1
3.
4
5.
Find  e
kx
dx .
1.
1 kx
e c
kx
4.
e c
kx
2.
1 kx
e c
k
5.
1
0%
0%
0%
5
ke  c
0%
3
0%
kx
2
3.
4
Don’t know
Integrate  x
1.
 1 12
x c
2
2.
 2 3 2
x c
3
1
2
dx .
4.
1 12
x c
2
5.
0%
0%
5
0%
3
2x 2  c
1
1
0%
2
0%
4
Don’t know
3.
Integrate  6
t dt .
1.
3.
2 32
t c
3
2
c
5.
Don’t know
0%
0%
0%
0%
0%
5
3 23
t c
2
9t
3
4
2.
4.
3
c
2
2
1
4t
3
 [ f ( x)  g ( x)]dx   f ( x)dx   g ( x)dx
1. True
2. False
3. Don’t know
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no
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k
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Tr
ue
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b
a
a
b
 f ( x)dx   f ( x)dx
1. True
2. False
3. Don’t know
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Integrate  (3 sin x 
x )dx .
1.
2 32
 3 cos x  x  c
3
4.
3 32
3 cos x  x  c
2.
2
3
2 2
3 cos x  x  c
3
5.
None of these
0%
0%
5
0%
3
0%
2
0%
1
2 32
 (3 cos x  x )  c
3
4
3.
Integrate  (t  2) 2 dt .
1.
1
(t  2) 3  c
3
2.
3
t
 2t 2  4t  c
3
3.
3(t  2)  c
3
4.
3
0%
0%
5
0%
3
0%
2
Don’t know
0%
4
t t
  4t  c
3 2
1
5.
2
1.
Integrate  sinh tdt .
cosh t  c
2.
 cosh t  c
3.
 sinh t  c
0%
0%
5
0%
3
0%
2
Don’t know
0%
1
5.
1
c
cosh t
4
4.
3
Find  x 3 dx .
1.
81
c
4
3.
0
2.
81
4
9
4.
0%
0%
0%
5
1
Don’t know
0%
3
0%
2
5.
4
27

Find  cos xdx .
0
2
Evaluate  e x dx.
1

Evaluate  e x dx .
0
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
1.
integrals?
dv
du
 u dx dx  uv   v dx dx
2.
dv
dv
 u dx dx  uv   u dx dx
3.
dv
du
 u dx dx  uv  v dx dx
0%
4
0%
3
0%
2
dv
dv
 u dx dx  uv  u dx dx
0%
1
4.
Integrate  ( x  2) sin xdx .
1.
 ( x  2) cos x  sin x
2.
 ( x  2) cos x  sin x
3.
( x  2) cos x  sin x
4.
0%
0%
0%
5
0%
3
1
None of these
0%
2
5.
4
( x  2) cos x  sin x
Find  3x e dx .
2 x
1.
3x e  6 xe  6e  c
2 x
x
x
2.
3x 2e x  6 xex  6e x  c
3.
3x 2e x  6 xex  6e x  c
4.
0%
0%
0%
5
0%
3
1
Don’t know
0%
2
5.
4
3x 2e x  6 xex  6e x  c

Evaluate  x cos xdx .
0
1
Evaluate  3x 2e x dx .
0
2
Evaluate  ( x  4) cos xdx.
1
Use a suitable substitution to find
cos
x
sin
xdx
.

2
1.
1
3
cos x  c
3
2.
 cos x  c
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0%
0%
0%
5
Don’t know
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4
5.
1
2
cos x  c
2
3
4.
2
1 3
cos x  c
3
1
3.
2
Use a suitable substitution to find
4  t sin( t  7)dt .
3
1.
4
 cos(t 4  7)  c
2.
3.
1
 cos( t 4  7)  c
4
1
4
cos( t  7)  c
4
0%
0%
0%
5
1
0%
3
0%
5.
2
cos(t  7)  c
Don’t know
4
4
4.
4
Evaluate the integral  t
2
3
sin t dt
by
1
making a suitable substitution.
6
Evaluate
8
(
3
x

2
)
dx by

1
making a suitable
substitution.
Which substitution would be most
helpful to evaluate the integral
ux
x dx ?
3
2.
3.
ux
2
x3
4.
0%
0%
0%
4
0%
3
None of these
2
ue
2
1
1.
e
x3
Which of the following is an incorrect
step when finding the definite integrand
6
x
1  x dx by the substitution method.
2
0
2.
1
u du

20
4.
Don't Know
5.
1
None of the above
0%
0%
0%
0%
0%
5
6
4
3.
du
 xdx
2
3
u  1 x
2
2
1.
Find
1.
6x  2
ln 2
c
3x  2 x  1
6x  2
dx
2
 3x  2 x  1 .
4.
ln 6x  2  c
2.
3x  2 x  1
ln
c
6x  2
2
3.
ln 3 x  2 x  1  c
0%
0%
0%
0%
0%
5
Don’t know
4
5.
3
2
1
2
1
Evaluate
t
0 t 2  1 dt
.
Express 
2
dx in partial fractions.
2
x x
1.
2
 2
  x  1  x dx
2.
3.
2 
2
  x  x  1 dx
2 
1
  x  x  1 dx
0%
0%
5
0%
3
0%
2
Don’t know
0%
1
5.
2 
2
  x  x  1 dx
4
4.
Express
4x 1
 3x 2  5 x  2dx
in partial fractions.
1.


1
9
  7(3x 1)  7( x  2) dx
2.
 7
7 
  3x 1  9( x  2) dx
3.
 1
9 
  3x 1  7( x  2) dx
0%
0%
5
0%
3
0%
2
Don’t know
0%
1
5.

9
1 

  7(3x 1)  7( x  2) dx
4
4.
Evaluate
3
1
1 ( x  1)(x  5)dx.
Evaluate
6
1
2 x 2  xdx.
If a carrot has been chopped into n
small pieces and the ith piece is Δxi
millimetres long, then the
total
length
of
n
the string is  xi .
i 1
1. True
2. False
3. Don’t know
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If g is continuous
on the interval
n
[m, n], then  g (t )dt is a number.
m
1. True
2. False
3. Don’t know
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If the derivatives of f and g are the
same then f=g.
1. True
2. False
3. Don’t know
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