MATH 152 Midterm: MATH 152 TAMU 2015a X1H Solutions

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turquoisegnu128

31 Jan 2019

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Mon, 23/feb c(cid:13)2015 art belmonte: use the substitution rule to nd the most general antiderivative. 5 du = dx: let u = x4 + 2. Then du = 4x3 dx or 1: hence r x3 cos(cid:0)x4 + 2(cid:1) dx = 1. 4 sin(cid:0)x4 + 2(cid:1) +c: use the substitution rule to compute the de nite integral. Show your steps by hand. (check with your calculator, if desired. ) Then du = 5 dx or 1: now u (1) = 2 and u (2) = 7, thus r 2. 2: find the area of the region enclosed by y = 5x + 30, intersections: when 5x + 30 = x3 + 2x2 24x, we have y = 6, 1, 5, area: r 5. 6(cid:12)(cid:12)(5x + 30) (cid:0)x3 + 2x2 24x(cid:1)(cid:12)(cid:12) dx. = 5581: find the area of the region bounded by x = y + 1 and x = 1.

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

Find the volume V formed by rotating the region enclosed by thecurves:

y^3=x andx=10y with y greater than or equal to 0; about they-axis.
V =

Find the volume of the solid obtained by rotating the regionbounded by the curves:
y=x^2/4, x=2y^2; about x=-5
V=
y=x^2V=

Usethe method of cylindrical shells to find the volume of the solidobtained by rotating the region bounded by the curves y=x^2, x=2,x=3;about the linex=6.

V=integral from 2 to 3(_________)dx=_________

#19 ï¼answer 13pi/3ï¼

MATH 152 Midterm: MATH 152 TAMU 2015a X1H Solutions

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