judd (aj22488) 5.3 Fundamental Theorem of Calculus spice (56140)
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judd (aj22488) LM 0: The FTC spice (56140)
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001
10.0 points
Evaluate the integral
3
1 + 4y y 2 dy .
I=
0
1
1. g (x) =
judd (aj22488) LM 1: The Net Change Theorem spice (56140)
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001
1
1
1. I = 4x 12x 4 + C correct
2. I = 4x
10.0 points
judd (aj22488) LM 2: Substitution spice (56140)
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001
10.0 points
Determine the integral
8 x x2 + 4
I=
3. I = cos(1 t3
judd (aj22488) LM 3: Area between Curves spice (56140)
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001
10.0 points
Find the bounded area enclosed by the
graph o
judd (aj22488) LM 4: Volumes spice (56140)
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001
10.0 points
Find the volume of the frustrum of the right
circular con
judd (aj22488) LM 5: Integration by Parts spice (56140)
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1. I =
7
e8
3. I = 1 +
8
e7
4. I = 1 +
7
e8
5. I = 1
7
e7
6
judd (aj22488) LM 6: Trig Integrals spice (56140)
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001
I=
1
4. I =
2
5. I =
1
1
4
Explanation:
Since
10.0 points
6.
judd (aj22488) LM 7: Trig Substitution spice (56140)
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001
1
Thus
I2 = 2 u +
1
sin 2u
2
/2
0
= .
Consequently,
10.0 p
judd (aj22488) LM 8: Partial Fractions spice (56140)
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001
Rewrite the expression
f ( x) =
x2
3x
3x + 2
using partial
judd (aj22488) LM 9: Strategies of Integration spice (56140)
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Evaluate the denite integral
/4
I=
1. I =
I=
0
1. I =
judd (aj22488) 11.2 Series spice (56140)
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judd (aj22488) 11.1 Sequences spice (56140)
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judd (aj22488) 5.4 The Indenite Integral and Net Change spice (56140)
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judd (aj22488) 5.5 Substitution spice (56140)
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judd (aj22488) 6.1 Area spice (56140)
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judd (aj22488) 6.2 Volume spice (56140)
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judd (aj22488) 7.1 Integration by Parts spice (56140)
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judd (aj22488) 7.2 Trigonometric Integrals spice (56140)
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judd (aj22488) 7.3 Trigonometric Substitution spice (56140)
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judd (aj22488) 7.4 Partial Fraction Decomposition spice (56140)
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judd (aj22488) 7.5 Strategy for Integration spice (56140)
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judd (aj22488) 7.8 Improper Integrals spice (56140)
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judd (aj22488) LM 10: Improper Integrals spice (56140)
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001
(ii) f has a vertical asymptote at one or
more of x = a,