MATH 233 Midterm: ExamNote3
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Worksheet by Kuta Software LLC
Calculus
Assignment
Name___________________________________ ID: 1
Date________________ Period____
-1-
For each problem, use the method of cylindrical shells to find the volume of the solid that
results when the region enclosed by the curves is revolved about the given axis.
1) x = y − 4, x = y2 − 8y + 16
Axis: x = 3
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
2) x = 2, x = y − 1, y = 1
Axis: x = 2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
3) x = 1, x = y3, y = 0
Axis: x = −1
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
4) x = y − 2, x = y2 − 4y + 4
Axis: x = −2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
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Worksheet by Kuta Software LLC
-2-
5) x = y − 1, x = y2 − 2y + 1
Axis: x = 5
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
6) x = 2, x = y − 1, y = 1
Axis: x = 5
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
7) x = 1, x = y − 2, y = 2
Axis: x = 4
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
8) x = y3, x = 0, y = 1
Axis: x = −3
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
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Worksheet by Kuta Software LLC
-3-
9) x = 1, x =
(
y − 2
)
2, y = 2, y = 3
Axis: x = −1
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
10) x = 1, x = y − 2, y = 2
Axis: x = −2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
For each problem, approximate the area under the curve over the given interval using 4
trapezoids.
11) g = r2
2 + 1; [−4, 4]
r
g
−8−6−4−2 2468
2
4
6
8
10
12
14
12) f = t2
2 + t + 2; [−5, 3]
t
f
−8−6−4−2 2468
2
4
6
8
10
12
14
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Document Summary
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