Thursday

October 8, 2015
Number of results: 6,527

**Calculus**

Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded by the curve y=x^2, below by the x-axis, and on the right by the line x=1, about the line x=-2
*January 24, 2012 by Becca*

**Math**

Find the volume of the solid generated by revolving the following region about the given axis The region in the first quadrant bounded above by the curve y=x^2, below by the x-axis and on the right by the line x=1, about the line x=-4
*September 11, 2012 by jake*

**Calculus**

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. The region R is the base of a solid. For this solid, the cross sections, perpendicular to the spx-axis, are rectangles ...
*April 19, 2015 by Anonymous*

**college, math**

find the bolume of the solid generated by revolving the region bounded by the graphs of y=sqrt x , y=0, and x=4 about the x axis
*April 29, 2010 by denise*

**Calculus**

Determine the volume of the solid formed by rotation about the x-axis of the region bounded by the curves y=4^x-1 and y = 21x on the interval 0<x<3.
*January 30, 2011 by Alex*

**calculus**

Determine the volume of the solid formed by rotation about the y-axis of the region bounded by the curves y=4^x-1 and y = 21x on the interval 0< x<3.
*January 30, 2011 by Jamal*

**calculus**

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = 6 − x y = 0 y = 5 x = 0
*January 23, 2012 by ME*

**Calculus**

Use the disk method to find the volume of the solid generated when the region bounded by 4= 1/(fourth root of (1-11x)), y=0, x=0, and x=1/22.
*January 24, 2012 by Becca*

**Calculus**

Let R be the region bounded by y=x^2, x=1, and y=0. Use the shell method to find the volume of the solid generated when R is revolved about the line y=-2.
*January 29, 2012 by Becca*

**Calculus**

Let R be the region bounded by y=x^2, x=1, and y=0. Use the shell method to find the volume of the solid generated when R is revolved about the line x=-11.
*January 29, 2012 by Becca*

**Math**

Find the volume of the solid generated by revolving the region bounded by y= 5 cosh (x) and y= 5 sinh (x) between x = 0 and x = 1 about the x-axis
*February 10, 2012 by Jose*

**calculus**

sketch the region R bounded by the graphs of the equations, and find the volume of the solid generated if R is revolved about the x axis when y=x^2 y=4-x^2
*May 1, 2012 by dario*

**calculus**

Sketch the region R bounded by the graphs of the equations and find the volume of the solid generated if R is revolved around the x axis. x= y^2 x-y =2
*May 1, 2012 by casquibaldo*

**calculus **

find the volume of the solid generated by revolving the region bounded by the graphs of the equations y=2sqrtx, y=o, x=3 about the x-axis.
*May 2, 2012 by carlton*

**Calculus**

Find the volume or the solid generated by revolving around the region bounded by the graphs of the equations about line x=6. xy=6, y=2, y=6, and x=6
*May 28, 2012 by Christina*

**Calculus**

Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis.
*January 30, 2013 by Liz*

**calculus**

Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis.
*January 30, 2013 by Liz*

**calculus**

Use the shell method to find the volume of the solid formed by rotating the region bounded by y=x^3, y=0, x=0, and x=2 about the line x=3.
*January 30, 2013 by Liz*

**Calculus**

Use the disk method to find the volume of the solid formed by rotating the region bounded by y=2x and y=x^2 about the y-axis
*February 4, 2013 by Liz*

**calculus**

Use the shell method to find the volume of the solid formed by rotating the region bounded by y=x^3, y=0, x=0, and x=2 about the line x=3.
*February 4, 2013 by Liz*

**calculus**

he volume of the solid obtained by rotating the region bounded by x=(y−2)^2 and y=x about the x-axis has the form N/2π. What is the value of N?
*July 18, 2013 by andy*

**calculas(URGENT..... PLEASE....)**

1) A region is bounded by the line y = x and the parabola y = x2 - 6x + 10. What is the volume of the solid generated by revolving the region about the x-axis? would u please give the explanation with a detailed steps to the answer because i am not able to reach the final ...
*April 12, 2011 by arun*

**Calculus**

Let R be the region bounded by the y-axis and the curves y = sin x and y = cos x. Answer the following. a)Find the exact area of R. b)A solid is generated by revolving R about the x-axis. Find the exact volume of the solid.
*March 23, 2012 by ronnieday*

**Calculus**

Let R be the region bounded by the y-axis and the curves y = sin x and y = cos x. Answer the following. a)Find the exact area of R. b)A solid is generated by revolving R about the x-axis. Find the exact volume of the solid.
*April 20, 2012 by ronnieday*

**Calculus [Finding volume of solid]**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2 y=0 x=3 about the y-axis
*November 30, 2012 by Ali*

**Calculus**

Let R be the square region bounded by y = 2, x = 2, and the x and y-axes. When R is rotated about the x-axis, what is the volume of the resulting solid? What is the volume of the solid generated by rotating R about the y-axis?
*December 1, 2011 by Macy*

**calculus**

Using a double integral, find the volume of the solid that's bounded by the cylinder z=x^2 and below by the region enclosed by the parabola y=2-x^2 and the line y=x
*November 3, 2009 by john*

**calculus II**

Consider the solid obtained by rotating the region bounded by the given curves about the line y = 2. Y = 2+secx -pi/3<= x <= pi/3 , y = 4 Find the volume
*February 17, 2010 by JILL*

**Calc**

The volume of the solid formed by revolving the region bounded by the graph of y = (x-3)² and the coordinate axes about the x-axis is given by what integral?
*January 2, 2011 by Erica*

**Calculus**

Use the disk method to find the volume of the solid generated when the region bounded by y=15sinx and y=0, for 0 </= x </= pi, is revolved about the x-axis.
*January 24, 2012 by Becca*

**Calculus Voulme**

find the volume of the solid generated by revolving the region r bounded by the graphs of the given equations about the y-axis. x^2+y^2=1 x=1 y=1
*July 19, 2012 by Laurie*

**Calculus - HELP URGENT PLEASE**

The region R is bounded by the x-axis, x=2 and y=x^2. Which of these expressions represents the volume of the solid formed by revolving R about the line x=2?
*August 9, 2015 by Ashley*

**Calculus (Volume of Solids)**

A solid has, as its base, the circular region in the xy-plane bounded by the graph of x^2 + y^2 = 4. Find the volume of the solid if every cross section by a plane perpendicular to the x-axis is a quarter circle with one of its radii in the base.
*March 13, 2012 by Casablanca*

**Calc**

The region bounded by y=2.5x^2 and y=4x is to be rotated about both axes and the volume generated calculated by both the washer and the shell methods. 1)The volume of the region bounded by y=2.5x^2 and y=4x, when rotated about the x-axis is? 2) The volume of the region bounded...
*September 16, 2012 by l*

**Calculus**

A solid has as its base a circular region in the xy plane bounded by the graph of x^2 + y^2 = 4. Find the volume of a solid if every cross section by a plane perpendicular to the x-axis is an isosceles triangle with base on the xy plane and altitude equal to the length of the ...
*September 11, 2010 by Denise*

**calculus**

Find the volume of the solid generated by revolving the region about the given line. The region is in the first quadrant bounded above by the line y= sqrt 2, below by the curve y=secxtanx, and on the left by the y-axis. Rotate the region about the line y=sqrt 2. i also need to...
*May 23, 2011 by ashley*

**Math**

Find the volme of the solid generated by revolving the region bounded by the triangle with vertices (1,1) (1,3) and (2,3) about the x axis using shells and washers.
*September 30, 2010 by Danielle*

**Calculus I**

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y=7x^5 y=7x, x is greater than or equal to 0
*April 30, 2013 by Anonymous*

**Math**

Find the volume of the solid that is obtained when the region bounded by the curves x=9-y^2, x=y^2+1 and y=0 is rotated about the line y=-2. (the upper shape above the x-axis)
*February 22, 2015 by Samantha*

**calculus**

Find the volume of the solid generated by revolving the region about the given line. The region in the second quadrant bounded above by the curve y = 16 - x2, below by the x-axis, and on the right by the y-axis, about the line x = 1 I have gathered, that washer method is to be...
*April 12, 2013 by Tiffany*

**Calculus**

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)
*March 27, 2008 by Sun*

**Calculus**

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y=ln x, y=0, x=1, x=3 Please show the steps in your work, thanks! :)
*March 29, 2008 by Pan*

**math-cal.**

find the volume of the solid formed by revolving the region bounded by the graph of y=2x^2+4x and y=0 about the y- axis ( express the answernin terms of pie)
*February 2, 2010 by Nancy*

**Math (Calculus)**

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. (Use Disc Method) y=3(2-x), y=0, x=0
*May 8, 2014 by Sherman*

**Calculus 2**

use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. xy=1, x=0, y=1, y=3
*August 30, 2014 by Dib*

**CALCULUS**

Let R be the region bounded by y=e^x, y=2. and the y-axis. Find the volume of the solid obtained by rotating the y-axis.
*November 15, 2012 by Sarah*

**calc2**

Let R denote the region in the plane consisting of all points (x,y) where x ≥ 1 and 0 ≤ y ≤ 2/x. Let S denote the solid formed by rotating R about the x-axis. Observe that S is an unbounded region; that is, it extends indefinitely in the direction of the ...
*March 8, 2012 by Anon*

**math**

Find the volume of the solid generated by revolving the region bounded by y= x^(1/2), y= 0, and x= 3 revolving around the y-axis.
*September 1, 2012 by Danelle*

**calc volume**

find the volume of a solid formed when the region bounded by y = e^(x-3) and y = 1 + ln(x) is rotated about the y-axis.
*December 19, 2012 by mary*

**Calculus **

5. Find the volume of the solid generated by revolving the region bounded by y = x2, y = 0 and x = 1 about (a) the x-axis (b) the y-axis
*June 5, 2013 by Maryam*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by the curves about the line x=-3, y=x^2, x=y^2. I keep getting the wrong answer!! Please hellpp!! =(
*December 15, 2010 by Anonymous*

**calculus**

Set up the integral that would be used to find the volume of the solid obtained by rotating the region bounded by y=x^3 , y=8, and x=0 about the x=-4. use disk/washer method.
*May 6, 2013 by diego *

**math calculus**

The volume of the solid obtained by rotating the region bounded by y=x^2−2x and y=x about the line y=9, has the form a/bπ, where a and b are positive coprime integers. What is the value of a+b?
*July 17, 2013 by andy*

**Calculus **

Consider the solid obtained by rotating the region bounded by the following curves about the line x=1. y=x,y=0,x=4,x=6 Find the volume So it would be pi (integral from 3 to 6) of ((1-y)^2 -(1-0)^2) right? so then you integrate it and get pi(Y^3/3-y^2) from 3 to 6. ?
*January 29, 2014 by christina*

**geometry**

Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless to say, your first task should be to ...
*March 18, 2013 by borat*

**geometry**

Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless to say, your first task should be to ...
*March 18, 2013 by borat*

**math**

Consider the region in Quadrant 1 totally bounded by the 4 lines: x = 3, x = 9, y = 0, and y = mx (where m is positive). Determine the value of c such that the vertical line x = c bisects the area of that totally bounded region. Needless to say, your first task should be to ...
*March 19, 2013 by borat*

**AP Calculus**

Let R be the region bounded by the x-axis and the graph of y=6x-x^2 Find the volume of the solid generated when R is revolved around the y-axis
*April 22, 2012 by Kelsey*

**Calculus **

Find the volume of the solid formed by revolving the region bounded by the graphs of y=4x^2 and y=16 about the x-axis. (Washer Volume)
*January 31, 2010 by john*

**calculus**

Give the volume of the solid generated by revolving the region bounded by the graph of y=ln(x), the x-axis, the lines x=1 and x=e, about the y-axis
*March 4, 2010 by josh*

**Volume **

Find the volume of the solid generated by revolving the region bounded by the given curves and line about the y-axis. y=50-x^2 y=x^2 x=0
*July 19, 2012 by Jamie*

**calculus**

Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real constant. a. Determine all values of c for which the graphs intersect in two distinct points. b. suppose c = -3/2. Find the area of the region enclosed by the two curves. c. suppose c = 0. Find the volume of the...
*March 23, 2010 by mary*

**math**

Finf the volume of the solid generated by revolving the region bounded by the curve. x=2/(y+1), x=0, y=0, y=3, about y-axis. My ans is pie unit^3. Is it correct? if wrong can i know the right calculation.
*December 20, 2012 by ifi*

**Calculus**

Let R be the region bounded by the curve x=9y-y^2 and the y- axis. Find the volume of the solid resulting from revolving R about the line y= -6. I believe the integral limits are from y=0 to y-9 i set up h(x) = 9y-y^2 r(x) = y+6 I am not sure if this is correct Can anyone help...
*December 4, 2013 by Salome*

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=1/x^4, y=0, x=2, x=9; about y=–5
*October 20, 2009 by Jessica*

**Calculus**

The base of a solid is the region bounded by the parabola y^2=4x and the line x=2. Each plane section is perpendicular to the x-axis is a square. What id the volume of the square?
*April 3, 2011 by Amanda*

**Calc**

find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=x^2+1; y=9-x^2; about y=-1
*December 15, 2011 by Ashley *

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: y=x, y=x^(1/2); about x=2
*February 28, 2012 by Heather*

**Calc2**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x2, y = 1; about y = 6
*March 2, 2012 by Cait*

**calculus one**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^4,y=1; about y=5
*April 8, 2010 by lssa*

**Calculus ll - Volumes**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=e^(-x), y=1, x=2; about y=2.
*October 7, 2010 by Abby*

**calculus**

Let R be the region in the first quadrant bounded by the graphs of y=e^-x, y=1/2x+1, and x=2. Then find the volume of the solid when R is revolved about each of the following lines... the x axis, y=-1, y=2, the y axis, x=-1, and x=3.
*December 15, 2010 by Drew*

**math**

Which of the following integrals computes the volume of the solid formed by revolving the region bounded by the graph of y = Ln(x), the x-axis, and the line x = 3 about the line x = 3?
*April 27, 2011 by anonymous *

**Calculus BC**

Let the region bounded by x^2 + y^2 = 9 be the base of a solid. Find the volume if cross sections taken perpendicular to the base are isosceles right triangles. (a) 30 (b) 32 (c) 34 (d) 36 (e) 38
*December 19, 2012 by Misha*

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y=4,x=5−(y−1) 2 ;
*October 1, 2014 by jo*

**math**

Find the volume of a solid generated by revolving the region bounded by y=secx and y=0 and x=0, x-pi/4 about the x axis. Don't evaluate. Please help!!!! Also, what si the average value of this equation? I don't understand what that means.
*April 17, 2011 by olivie*

**Math Calc 1 Last question **

Find the volume of the solid obtained by rotating the region bounded by the curves y=4x-x^2, y=8x-2x^2 about the line x=-2. I got 256 pi/3 but pretty sure my work is wrong.
*December 12, 2012 by Anonymous*

**Calculus**

"Find the volume of the solid generated by revolving the region bounded by the graphs of the given equations about the indicated lines: y = 2x^2 y = 0 x = 2 About the line y = 8"
*April 18, 2010 by Stuck*

**calculus**

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations and/or inequalities about the indicated axis. x = y(25 − y2)^1/2 x = 0 the y-axis
*February 2, 2011 by Morgan *

**Calculus**

Find the volume of the solid generated by the region in the first quadrant bounded above by the 3x+y=6, below by the x-axis, and on the left by the y-axis, about the line x= -2.
*June 3, 2012 by Liz*

**Math**

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = (64 − x^2)^(1/4), y = 0, x = 6, x = 7; about the x-axis
*January 21, 2013 by Em*

**Math**

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. x = (y − 6)^2, x = 1; about y = 5
*January 24, 2013 by Em*

**calculus help**

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4 − 1/2x, y = 0, x = 0, x = 1; about the x-axis V = ????
*May 3, 2014 by Anonymous*

**Calculus**

Find the area of the region bounded by the line y=3x and y= x^3 + 2x^2? and find the area of the region bounded by the curve y=e^2x -3e^x + 2 and the x-axis?
*May 10, 2011 by Akansha*

**calculus 1**

can you please help me, i'm really confused Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. y= 20sqrt y, x=0, y=1
*May 5, 2010 by Miya*

**Calc Jacobian**

Thanks "I know that the xy region is the line x=y y=0 and y=1- x/2)" It is helpful to rewrite the region in the x-y plane by specifying the three lines and the endpoints, i.e. the points where they intersect. If you insert these points in the formula for U and V you obtain the...
*December 4, 2006 by Rob*

**cal**

Solve the problem. Find the volume of the solid generated by revolving the region bounded by the curve y=lnx, the x-axis, and the vertical line x=e^(2) about the x-axis.
*December 23, 2013 by tony*

**calculus help**

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. x = 4(square root of (3y)), x = 0, y = 3; about the y-axis V=?????
*May 3, 2014 by Christine *

**Calculus**

Find the volume of the solid formed by rotating the region enclosed by y=e^(1x)+4 y=0 x=0 x=0.3 about the x-axis. I attempted this problem numerous time and kept on getting 5.501779941pi, using the formale integral of pi(r^2) bounded by 0.3 and 0.
*August 28, 2012 by Huey*

**AP Calc**

Find the volume of the solid generated by rotating the region bounded by the graph of y=x^2, y=0, x=1, and x=3 about the line parallel to the x-axis and one unit below it. Please help I have no idea how to solve this problem.
*March 1, 2015 by anonymous*

**Calculus**

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where 1<=a<5. Using your calculator, find a. 3...
*February 27, 2013 by Jessy152*

**calculus**

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 a)the line x = 4
*January 25, 2012 by ReinaS*

**Ap calc**

Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. x + y = 3, x = 4 − (y − 1)^2
*February 19, 2015 by Emma*

**AP Calc**

The base of a solid is the region in the first quadrant bounded by the ellipse x^2/a^2 + y^2/b^2 = 1. Each cross-section perpendicular to the x-axis is an isosceles right triangle with the hypotenuse as the base. Find the volume of the solid in terms of a and b. I'm having ...
*March 17, 2014 by Anon*

**Math (Calculus)**

Use the disc method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y=x^3, y=0, x=2 a)the x-axis b)the line x=4
*May 9, 2014 by Sherman*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by the curves: y = x^2 and x = y^2 about the line y = 1. I received the answer pi/30, using the outer radius of (1 - x^2) and the inner radius of (1 - x^(1/2)). Is this correct?
*November 23, 2014 by Joshua*

**Calculus**

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(ex) is rotated about the x-axis. What is the volume of the generated solid? Got 2.8 and .79 very confused
*August 4, 2015 by Ali*

**calculus**

10). Find the area of the region bounded by the graph of f(x)=4lnx/x, y=0, x=5.8 11). Find the area of the region bounded by x=y^2-1y, x=0
*April 14, 2013 by Sally*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by the curves: 2x = -y^2 y^2 = -x + 2 y = 0 for y >= 0 about the x-axis. Not sure how to do this one, could anybody help me identify what this looks like and how to identify the outer/inner radius? Thanks
*November 23, 2014 by Joshua*

**calc**

If D is the solid region in the first octant bounded above by the paraboloid z = 1 − x2 − y2 and below by the xy-plane, the volume of D is: so i set this up integrating over dz dr dtheta and got pi/2 but the answer i spi/8
*December 7, 2014 by rebecca*