Please calculate the volume using shell rule 9. The region bounded by the graphs of y² = x, x=0, y=-1, and y=1 is revolved about the line y-2. Find tvolume of the resulting solid.

Answered: Image /qna-images/answer/77be1d1e-74df-47f2-b0cb-40a705489795.jpg

Answered: 9. The region bounded by the graphs of…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 25E

See similar textbooks

Similar questions

Find the exact volume of the solid that results when the region bounded in quadrant I by the axes and the lines x=9 and y=5 revolved about the a x-axis b y-axis
Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.
4. A 3D solid has base that sits in the x-y coordinate plane. That base is a triangle with vertices (4, 0), (-4, 0), (0, 8). Cross sections perpendicular to the y-axis are semi-circles with diameter in the plane. The volume of the solid is given by A. * 7(8 – 2x)² dx B.,(2x + 8)? + f, (8 – 2x)²dx C. (8 – y)? dy D. (8 - y)? dy E. (8 – y)? dy 0 8 -8 T 0 4 -8 T 0 2
3. Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = 5x2 y = 0 x = 3 (a) the y-axis (b) the x-axis (c) the line y = 45 (d) the line x = 3
Determine a region of the xy-plane for which the given differentail equation would have a unique solution whos graph passes through point (x,y) in the region. (y-x)y' = y +x
7. The region bounded by the curves y = x²+2x+3 and the line y = 2x+7 is revolved about the x-axis to generate a solid. Find the volume of the solid.
Find the center of mass of a thin plate of constant density 8 covering the given region. The region bounded by the parabola y = 3x - 3x² and the line y = - 3x The center of mass is (Type an ordered pair.)
The arc of the parabola y = x sq. from ( 1,1, ) to ( 2, 4 ) is rotated aboutthe y -axis. Find the area of the resulting surface
. A pool, when viewed from above, is in the shape of an ellipse whose equation is given by (x ^ 2)/144 + (y ^ 2)/49 = 1 A) solve the given equation for y B) Use integration techniques from chapter 5 and/or 7 to compute the area of the ellipse. Hint: Compute the area of the part of the ellipse in quadrant I. Then, multiply your answer by 4 to get the area of the entire ellipse. The units for the area in this problem are in f * t ^ 2 C) Suppose the pool is 10 feet deep and has the shape of an ellipse throughout (an elliptical cylinder). Further, suppose the pool currently has 9 feet of water. Find the work done to pump all of the water out of the pool To do this, first set this up as a Riemann sum, finding the work W_{i} required to pump the slice of water, of width Delta*x out of the pool. Then, set up the corresponding integral and integrate to find the work done to pump all of the water out of the pool. Use the fact that water weights 62.5 lbs / f * t ^ 3
2. The curve determined by the equation y2 = x²(x + 3) intersects itself, forming a loop. Find the area enclosed by this loop.
5. Consider the two curves y = 2. = x° – 3.x4 + 20x + 88x² + 71x – 74 and y = 2.a + 50x – 22x² + 42x + 31. Find the following: (a) The points of intersection of these two curves. (b) The area of each region bounded by both curves. (c) The total area of the regions bounded by both curves.
find the region bounded by 255C and the line y=x area of the the parabolas

SEE MORE QUESTIONS

Recommended textbooks for you

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

SEE MORE TEXTBOOKS

9. The region bounded by the graphs of y² = x, x=0, y=-1, and y=1 is revolved about the line y-2. Find t volume of the resulting solid.