3. Base region is th. x+y = 4 %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please answer number 3
For Problems 1-4, set up (but do not integrate) integrals for evaluating the volumes of the
solids formed by the given cross sections. For Problems 3-6, sketch the graphs of the
regions before setting up the integrals used for finding the volumes.
1.
Base region bounded by y=x²,
2. Base region bounded by y=-x² +x
y = 0, and x=1 as shown.
and y=0 as shown.
y
0.5+
a. Squares
b. Semicircles
c. Rectangles with height 2
a. Squares
b. Equilateral triangles
c. Rectangles whose heights are
half of their bases
3.
Base region is the circle
4. Base region bounded by y=2-x
x'+y =4
a. Squares perpendicular to the
у-аxis
b. Semicircles perpendicular to
the y-axis.
and y=x
a. Squares perpendicular to the
х-ахis
b. Right triangles perpendicular to
the x-axis. The base of the
triangle sits in the region and the
height = 3 times the base.
Transcribed Image Text:For Problems 1-4, set up (but do not integrate) integrals for evaluating the volumes of the solids formed by the given cross sections. For Problems 3-6, sketch the graphs of the regions before setting up the integrals used for finding the volumes. 1. Base region bounded by y=x², 2. Base region bounded by y=-x² +x y = 0, and x=1 as shown. and y=0 as shown. y 0.5+ a. Squares b. Semicircles c. Rectangles with height 2 a. Squares b. Equilateral triangles c. Rectangles whose heights are half of their bases 3. Base region is the circle 4. Base region bounded by y=2-x x'+y =4 a. Squares perpendicular to the у-аxis b. Semicircles perpendicular to the y-axis. and y=x a. Squares perpendicular to the х-ахis b. Right triangles perpendicular to the x-axis. The base of the triangle sits in the region and the height = 3 times the base.
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