Sunday

May 24, 2015

May 24, 2015

Number of results: 6,369

**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 (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**

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*

**calculus**

The figure shows the region bounded by the x-axis and the graph of . Use Formulas (42) and (43)-which are derived by integration by parts-to find (a) the area of this region; (b) the volume obtained by revolving this region around the y-axis.
*May 29, 2010 by rene*

**math**

find the volume of the solid formed by revoving the region bounded by the graphs of y=absoulute value cosx, x=0, x=2pi, y+x=0 about y=2 after a lot of messy calculations I got 548.2 Do you have a numerical answer?
*April 30, 2007 by helpless*

**Algebra 2**

A retail lumberyard plans to store lumber in a rectangular region adjoining the sales office. The region will be fenced on three sides and the fourth side will be bounded by the wall of the office. Find the dimensions of the region if 350 feet of fencing is available and the ...
*May 22, 2012 by Carolyn*

**Calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=x^2, x=y^2 about the axis x=–1
*October 30, 2008 by Sam*