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MATH 032 Midterm: math30_2008s_exam1

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turquoisegnu128

9 Jan 2019

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Name: ________________________ class: ___________________ date: __________ id: a. Free response: sketch the region enclosed by y = 4 - x. Decide whether to integrate with respect to xor y. Find the area of the region: find the volume of the solid obtained by rotating the region bounded by y x and y x about the line y. = 0: the linear density of a 15 m long rod is (x) = 8 (3 + x)2 kg/m, where xis measured in meters from one end of the rod. Find the average density of the rod: use the method of cylindrical shells to find the volume of a solid obtained by rotating the region bounded by the given curves about the yaxis. y. Identify the choice that best completes the statement or answers the question. A spring has a natural length of 22 cm. F ( x ) = k ( x x )

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Related Questions

I need help solving some problems including area bounded by aregion and volume by cylindrical shells.

1) y = 3/x

y=12x

y=1/12x

x>0

2)
Find thevolume V of the solid obtained by rotating the regionbounded by the given curves about the specifiedline.

y=4-(1/2x)

y=0

x=2

x=3

rotated about xaxis

3)Find thevolume V of the solid obtained by rotating the regionbounded by the given curves about the specified line.
x = 4sqrt(5y)

x=0

y=3

rotated on y axis

4)Find the volume V of the solid obtained by rotatingthe region bounded by the given curves about the specifiedline.
y = ln3x

y =4

y =5

x = 0

rotated on yaxis

5)
Find the volume V of the solid obtained by rotating theregion bounded by the given curves about the specified line.

y =3x⁵

y =3x

x Ã¢â°Â¥ 0

rotated on X axis

6)
Find the volume V of the solid obtained by rotating theregion bounded by the given curves about the specifiedline.

y² = 2x
x = 2y

about the y-axis

7)A CAT scan produces equally spaced cross-sectional views of ahuman organ that provide information about the organ otherwiseobtained only by surgery. Suppose that a CAT scan of a human livershows cross-sections spaced 1.5 cm apart. The liver is 15 cm longand the cross-sectional areas, in square centimeters, are 0,17, 58, 79,95, 107, 118, 129, 64, 39,and 0. Use the Midpoint Rule with n = 5 to estimate thevolume V of the liver.

8)
Let S be the solid obtained by rotating the region shown inthe figure about the y-axis. (Assume a = 7 and b = 2.)
y=ax(x-b)^2
What are its circumference c and height h?
Use shells to find the volume V of S.

9) Let S be the solid obtained by rotating the region shownin the figure about the y-axis. (Assume a = 4 andb = 2.)
y=asin(bx^2)

What are its circumference c andheight h?
Use shells to find the volume V of S.

10)Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded by the given curves aboutthe y-axis.

y = 2x²
y = 12x Ã¢Ëâ 4x^2

11)Use the method of cylindrical shells to find thevolume of the solid obtained by rotating the region bounded by thegiven curves about the x-axis.

xy = 3
x =0
y =3
y =5

12)
Use the method of cylindrical shells to find the volume V ofthe solid obtained by rotating the region bounded by the givencurves about the x-axis.

x + y = 5
x = 9 Ã¢Ëâ (y Ã¢Ëâ 2)²

13)Use the method of cylindrical shells to find the volume Vgenerated by rotating the region bounded by the given curves aboutthe y-axis.

y = 5x²
y = 0
x = 1

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pearwater-buffalo150

1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 7x², y = 7x, x ? 0; about the x-axis

2. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y = 5 + sec x, (-pi/3 < x < pi/3), y=7; about y=5