# The parabola y x1tothepluujolay 2 xl o x 3 the solid

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Chapter 4 / Exercise 2
Numerical Analysis
Burden/Faires
Expert Verified
the parabola y = x:1tothePlUUJolay = 2 - x'l. , o x 3. The solid lies between planes perpendicular to the x-axis at x - - 1 and x - I. The cross-sections perpendicular to the x-axis between these planes arc squares whose bases run from the semi- circle y = - ~ to the semicircle y = ~. 4. The solid lies benwen planes perpendicular to the x-axis at x = -I and x = 1. The cross-sections perpendicular to the x-axis be- tween these planes ~s whose diagonals run from the semicircley = -VI - x 2 to the semicircley = ~. 5. The base of a solid is the :region between the ClU'Ve y = 2 ~ and the interval [0, 'Ir] on the x-axis. The cross-sections perpendi- cular to the x-axis are L cquilateIal. triangles with bases running from. the x-axis to the curve as shown in the accompanying figure. x b. squares with bases running from the x-axis to the curve. 6. The solid lies between planes perpendi.cular to the x-axis at x - -'lr/3 andx - 'lr/3. The cross-sections perpendicular to the x-axis are L circula:r disks with diameters running from the curve Y - tanxtothecurvey - secx. b. squares whose bases run from the curve Y - tan x to the curvey - secx. 7. The base of a solid is the region bounded by the graphs of Y - 3x, Y - 6, and x - O. The cross-sections perpendicular to the x-axis arc L rectangles of height 10. b. rectangles of perimeter 20. 8. The base of a solid is the region bmmded by the graphs of Y - v';; and Y - x12. The cross-sections perpendicular to the x-axis are L isosceles triangles of height 6. b. semi-circles with diameters running across the base of the solid 9. The solid lies between planes perpendicular to the y-axis at y = 0 and y = 2. The cross-sections perpendicular to the y-axis arc cir- cular disks with diamebml running from the y-axis to the parabola x _ Vsy2. 10. The base of the solid is the diskx 2 + y:1 S L The cross-sections by planes perpendicular to the y-axis between y = - 1 and y = 1 arc isosceles right triangles with one leg in the disk. , ---- ~---- o 11. Find the volume ofthc given tetrahedron. (Hint Consider slices perpendicular to one of tile labeled edges.) , , / 11. Find the volume of the given pyramid, which has a square base of area 9 and height 5. 13. A twisted lOUd A square of side length s lies in a plane perpen- dicularto alineL. One vertex of the square lies onL. As this square moves a distance II along L, the square turns one revolution about L to generate a carkscrew-li]re colmnn with square cross-sections. L Find the volmne of the colmnn. b. What will the volume be if the square turns twice instead of once? Give reasons foryom answer.
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Chapter 4 / Exercise 2
Numerical Analysis
Burden/Faires
Expert Verified
14. CJIYlIlisi'. principle A solid lies between planes perpendicular to the x-axis at x - 0 and x - 12. The cross-sections by planes perpendicular to the x-axis are circular disks whose diameters run from the line y - x/2 to the line y - x as shawn in the accompa- nying figure.