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region bounded by and the solid extends

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Calculus
find volume of solid obtained by rotating region bounded by curves y=x and y=sq.rt x, about line x=2

calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y=x^6, y=1 about the line y=4

Calculus
Find the volume of the solid formed by revolving the region bounded by y=x^3, x=2 and y=1 about the y-axis. Please help =(

calculus 2
find the volume of the solid obtained by revolving the region bounded by the graphs of y=2+4x-x^2 and y=2 about the line y=2.

Pre Calc
Find the volume of the solid formed by revolving the region bounded by y = 16 - x^2 and y = 0 about the x-axis .

calculus
help!! please ...Find the volume of the solid obtained by rotating the region bounded by y=5x+25 y=0about the y-axis

calculus
determine the volume of the solid of revolution generated by revolving the region bounded by y=x^3-x^5, y=0, x=0 and x=1 about the line x=3

calc
Find the volume of a solid formed by region R which is bounded by y = 1/(x^2+1) and y = -cos(x) and rotated about the line y = 3.

calc
Find the volume of a solid formed by region R which is bounded by y = 1/(x^2+1) and y = -cos(x) and rotated about the line y = -2.

calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.

Calculus
find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3 y=1 x=2 about the y-axis

calculus
Find the volume of the solid obtained by rotating the region bounded by the given curves about the line x=-3 y=x^2, x=y^2

Calculus
Compute the volume of the solid formed by revolving the fourth quadrant region bounded by y = x^2 - 1 , y = 0, and x = 0 about the line y = 6.

Calculus
Compute the volume of the solid formed by revolving the fourth quadrant region bounded by y = x^2 - 1 , y = 0, and x = 0 about the line y = 9.

calculus
find the volume of the solid obtianed by rotating the region bounded by the given curves about the line x=6 x=y^2 , x=1

Calculus I
Which of the following represents the volume of the solid formed by revolving the region bounded by the graphs of y =x^3, y = 1, and x = 2, about the line x = 2?

Calculus
The region in the first quadrant bounded by y=6x^2 , 2x+y=8, and the y-axis is rotated about the line x=-1. The volume of the resulting solid is:

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

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 ...

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

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

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.

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.

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

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.

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.

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.

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

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

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

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.

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

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.

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.

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.

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

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.

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?

Calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=π/2 about the line y=1.

Calculus - Integrals
Find the volume of the solid of revolution obtained by revolving region bounded by the parabolas 2y=x^2 and y^2=4x about the x-axis

Calculus
Which of the following integrals will find the volume of the solid that is formed when the region bounded by the graphs of y = ex, x = 1, and y = 1 is revolved around the line y = -2

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 ...

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.

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.

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

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?

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

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

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?

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.

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

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?

math
The base of a solid is the region bounded by the parabola x^2 = 8y and y=4. Each cross section perpendicular to the y-axis is an equilateral triangle. Find the volume.

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.

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 ...

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...

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...

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.

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

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)

Calculus
Use the disk method to find the volume of the solid generated by revolving about the y-axis the region bounded by the curves y=8−x^2 and the curve y=x^2.

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...

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! :)

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! :)

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)

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

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

Cal 2
The region bounded by y=3/(1+x^2), y=0, x=0 and x=3 is rotated about the line x=3. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are:

calculus
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 = 2, x = 0, y = 2, y = 4

calculus review please help!
Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5. Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = -x^3 and y = -x. A ...

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 ...

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.

geometry
Sketch the region enclosed by the lines x=0 x=6 y=2 and y=6. Identify the vertices of the region. Revolve the region around the y-axis. Identify the solid formed by the revolution calculate the volume of the solid. Leave the answer in terms of pi.

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.

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.

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

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!! =(

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.

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?

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. ?

Calculus
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2. A. 8pi/15 B. 32pi/15 C. 64pi/15 D. 4pi/15 E. 16pi/15

Calculus AP Exam review explanation pls
1)What is the area bounded by y = x^2 and y =3x? A)5 B)9/2 ***C)8 D)11.2 E)25 i believe it to be 8 but im not sure. 2)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...

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

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 ...

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 ...

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 ...

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)

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

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

Calculus
The region R is in the first quadrant and bounded by the x-axis, the y axis, and y= 3+2x-x^2. Find the volume of the solid that results when R is revolving about y+1= 0

K
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3e^(-x), y = 3, x = 2; about y = 6

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...

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.

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...

Please help Calculus
Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5.

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

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?

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

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

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

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