MATH 233 Study Guide - Midterm Guide: Butea Monosperma
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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 = 1, x =
(
y − 4
)
2, y = 4, y = 5
Axis: x = −3
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
2) x = y, x = y
2
Axis: x = −3
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
3) x = 4, x =
(
y − 3
)
2, y = 3, y = 5
Axis: x = −1
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
4) x = 2 − y, x = 0, y = 1
Axis: x = −4
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 − 2, x = y2 − 4y + 4
Axis: x = 2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
6) x = y3, x = 0, y = 1
Axis: x = 5
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
7) x = 4, x =
(
y − 3
)
2, y = 3, y = 5
Axis: x = −2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
8) x = 1, x = y3, y = 0
Axis: x = 2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
find more resources at oneclass.com
find more resources at oneclass.com
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Worksheet by Kuta Software LLC
-3-
9) x = y, x = y
2
Axis: x = 4
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
10) x = y3, x = 0, y = 1
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) r = t2 − 2t + 2; [−2, 2]
t
r
−8−6−4−2 2468
2
4
6
8
10
12
14
12) g = t2
2 + t + 1; [−6, −2]
t
g
−8−6−4−2 2468
2
4
6
8
10
12
14
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