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Compute
e^{sin(x)}cos(x)dx
.

(A)
e^{sin(x)} + C

(B)
cos(x) + C

(C)
e^{cos(x)} + C

(D)
e^{sin(x)}cos(x) + C

Find
tan(x)dx
.

(A)
log| cos(x)| + C

(B)
log| sin(x)| + C

(C)
-log| cos(x)| + C

(D)
log| tan(x)| + C

Compute
1/()dx
.

(A)
(3/2)

(B)
2/(3)

(C)
(2/3)

(D)
(2/3)

Compute
2sin(x)cos(x)dx
.

(A)
(2/3)

(B)
(2/3)(sin^{2}(x))^{3/2}

(C)
(2/3)(sin^{2}(x))^{3/2}cos(x)

(D)
(2/3)(sin^{2}(x))

Find

dx

(A)
- (cos^{2}())/2 + C

(B)
-cos^{2}() + C

(C)
-cos^{2}(1 + x^{2}) + C

(D)
(cos^{2}())/2 + C

Compute
x^{2}e^{x3+7}dx
.

(A)
e^{x3+7} + C

(B)
(1/3)e^{x3+7} + C

(C)
(1/3)e^{3x2
} + C

(D)
e^{3x2
} + C

In order to integrate a function that is a product of an easily integrable function with an
easily differentiable one, it is often useful to employ

(A)
the product rule.

(B)
the chain rule.

(C)
integration by parts.

(D)
change of variables.

The method of integration that is closely related to the chain rule for differentiation is the

(A)
integration by parts method.

(B)
change of variables method.

(C)
chain rule method for integration.

(D)
partial fraction decomposition.

Compute
5xe^{x}dx
.

(A)
5(x - 1)e^{x}

(B)
(5x - 1)e^{x}

(C)
(x - 5)e^{x}

(D)
5x - 5e^{x}

Compute
(log(x))^{2}/xdx
.

(A)
(log(x))^{3}/2 + C

(B)
x(log(x))^{3}/3 + C

(C)
x(log(x))^{3}/2 + C

(D)
(log(x))^{3}/3 + C

Find
- 4dx

(A)
8 - Π/2

(B)
8Π/2

(C)
4Π/2

(D)
4 - Π/2

Compute
3 - | x + 1|
dx
.

(A)
11/2

(B)

(C)

(D)
13/2

Determine the value of
Π/x^{2}dx
.

(A)
2Π

(B)
Π

(C)
Π^{2}

(D)
Π^{3/2}

Find
2
dx
.

(A)
7Π/2

(B)
13Π/2

(C)
7Π

(D)
5Π/2

Compute the area between the graphs of the functions
f (x) = x^{2} - 4x + 3
and
g(x) = - x^{2} + 4x - 3
.

(A)
8

(B)
12

(C)
8/3

(D)
3

Find the area between the graphs of
x^{2} - 3
and
2x - 3
.

(A)
4/5

(B)
3/4

(C)
8/3

(D)
4/3

Find the volume of the solid given by revolving the region below the graph of
6 - 3x
from
0
to
2
about the
y
-axis.

(A)
4Π

(B)
2Π

(C)
8Π^{2}

(D)
8Π

Compute the volume of the solid given by revolving the region below the graph of
x^{2} - 4x + 5
from
x = 0
to
2
about the
y
-axis.

(A)
20Π/3

(B)
40Π/3

(C)
10Π/3

(D)
10Π

Compute the volume of the solid given by revolving the region below the graph of
sin(x)
from
0
to
Π
about the
y
-axis.

(A)
4Π^{2}

(B)
2/Π^{2}

(C)
2Π^{2}

(D)
Π^{2}/2

Compute the volume of the solid given by revolving the region below the graph of
sin(x)
from
0
to
Π
about the
x
-axis.

(A)
Π^{2}/4

(B)
Π^{2}/2

(C)
Π^{4}/2

(D)
Π^{3}/2

Determine the volume of the solid given by revolving the region below the graph of
e^{2x}
from
x = 1
to
2
about the
x
-axis.

(A)
(Π/4)(e^{8} - e^{4})

(B)
Π(e^{8} - e^{4})

(C)
(Π/4)(e^{2} - e)

(D)
(Π/4)(e^{8} - e)

Compute the volume of the solid given by revolving the region below the graph of
f (x) = 2
from
x = - 2
to
1
about the
x
-axis.

(A)
24Π

(B)
12Π

(C)
12/Π

(D)
24/Π

Find
sin(x)e^{x}dx
.

(A)
(e^{x}/2)(sin(x) - cos(x)) + C

(B)
(e^{x}/2)(sin(x) + cos(x)) + C

(C)
(e^{x})(sin(x) - cos(x)) + C

(D)
(e^{x})(sin(x) + cos(x)) + C

Compute
x^{4}log(x)dx
.

(A)
(x^{5}/5)(log(x) - 1) + C

(B)
(x^{5}/5)(log(x) - 1/5) + C

(C)
(x^{5}/5)(log(x) - 5) + C

(D)
(x^{5}/5)(log(x) - 1/25) + C

Find the value of
cos^{2}(x)(1 + tan^{2}x)dx
.

(A)
e^{2}

(B)
2

(C)
1

(D)
sin(1)

Determine the radius of convergence of
5(- 1)^{n}x^{n}
.

(A)
Π

(B)
0

(C)
∞

(D)
1

What is the radius of convergence of
(x - 1)^{n}/n!
?

(A)
1

(B)
2

(C)
∞

(D)
1/2

Find the integral of
(- 1)^{n-1}x^{n}/n
(on its radius of convergence).

(A)
x^{n}(n - 2)!/n!

(B)
(- 1)^{n}x^{n}(n - 2)!/n!

(C)
(- 1)^{n}x^{n}(n - 3)!/n!

(D)
(- 1)^{n}x^{n}(n - 2)!/(n - 1)!

What is the value of
6(1/3)^{n}
?

(A)
9

(B)
11

(C)
10

(D)
5

Compute

dx

(A)
2 log(x - 1) - 3 log(x + 2) + C

(B)
2 log(x - 1) + 5 log(x + 1) + C

(C)
2 log(x - 1) + 5 log(x + 2) + C

(D)
2 log(x - 1) + 3 log(x + 2) + C

Compute

dx

(A)
log(x - 1) + 10 log(x + 1) + C

(B)
log(x - 1) + 8 log(x + 1) + C

(C)
2 log(x - 1) + 8 log(x + 1) + C

(D)
3 log(x - 1) + 8 log(x + 1) + C

Find

dx

(A)
2 log(x + 3) + log(x + 4) - 2x + C

(B)
2 log(x + 3) + log(x + 2) - 2x + C

(C)
2 log(x + 2) + log(x + 4) - 2x + C

(D)
2 log(x + 3) + 3 log(x + 4) - 2x + C

Compute

dx

(A)
-5 log(x + 2) + 3x + C

(B)
-5 log(x + 2) + 7 log(x) + 3x + C

(C)
-5 log(x + 2) + 7 log(x) + C

(D)
5 log(x + 2) + 7 log(x) + 3x + C

Compute
1/(x - 1)^{2}
.

(A)
1/(x - 1) + C

(B)
2/(1 - x) + C

(C)
x/(1 - x) + C

(D)
1/(1 - x) + C

Find
x/(x - 1)^{2}dx
.

(A)
- x/(1 - x) + log(x - 1) + C

(B)
x/(1 - x) - log(x - 1) + C

(C)
x/(1 - x) + log(x - 1) + C

(D)
- x/(1 - x) - log(x - 1) + C

It is possible for a series with positive terms to converge but not

(A)
converge absolutely.

(B)
have bounded partial sums.

(C)
have a ratio of consecutive terms that is always less that
1
.

(D)
have a least upper bound for its partial sums.

Determine the value of
1/(n log(n))
.

(A)
undefined

(B)
1/log(3)

(C)

(D)
1

Find
1/(x(log(x))^{2})dx
.

(A)
log(2)

(B)
1/log(2)

(C)
2/log(2)

(D)
4/log(2)

For which values of
k
does the series
4/(n + 1)^{k}
converge?

(A)
k≥1

(B)
k < 1

(C)
k > 1

(D)
k > 2

The Taylor series of a function is a kind of

(A)
alternating series.

(B)
harmonic series.

(C)
geometric series.

(D)
power series.

Find the length of the parametric curve
(3 + 2 sin(t), -1 + 2 cos(t))
from
t = 0
to
Π
.

(A)
2Π

(B)
Π

(C)
Π

(D)

How many petals are on the "flower" formed by the polar curve
r(θ) = sin(4θ)
?

(A)
2

(B)
6

(C)
4

(D)
8

What is the velocity vector to the parametric curve
(e^{t} + cos(t), 3t + 2)
at time
t = 2Π
?

(A)
(e^{2Π
} -2Πsin(t), 3)

(B)
(e^{2Π
}, 3)

(C)
(log(2Π), 3)

(D)
(log(2Π) - 2Πsin(t), 3)

Find the acceleration vector for the parametric curve
(sin(t)cos(t), log(t))
at time
t
.

(A)
(2 sin(t)cos(t), -1/t^{2})

(B)
(- 2 sin(2t), -1/t^{2})

(C)
(- 2 sin(2t), 1/t^{2})

(D)
(2 sin(2t), -1/t^{2})

Find the speed of the particle whose motion in the plane is given by
(log(27x^{2}), 3x)
.

(A)

(B)

(C)

(D)

Determine the area below the polar curve
r(θ) = 3θ^{2} + 2
from
θ = 0
to
1
.

(A)
26 sin(1)

(B)
53/11

(C)
49/10

(D)
53 sin(1)

Compute the area below the graph of the polar curve
r(θ) = e^{
θ
}
from
θ = 2
to
t
.

(A)
e^{2t} - e^{4}

(B)
(1/4)(e^{2t} - e^{4})

(C)
e^{2t} - e^{2}

(D)
(1/4)(e^{2t} - e^{2})

Find the area between the parametric curves
(t, t^{2} - 1)
and
(t, - t^{2} + 1)
.

(A)
4/3

(B)
1/3

(C)
2/3

(D)
8/3

The set of points on a unit circle could not be

(A)
the graph of a function.

(B)
a polar curve.

(C)
a parametric curve.

(D)
the curve defined by the velocity vectors of a parametric curve.

To derive the formula for the length of the parametric curve, one may