# region bounded by and the solid extends

7,583 results

**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 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

**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**

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

**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...

**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

**calculus 2**

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x, y = 0, x = 2, x = 6; about x = 1

**calculus**

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed line. x = 1−y^4, x = 0; about x = 1.

**calculus **

Find the volume of the solid obtained by rotating the region bounded by the given curves about the speciﬁed line. x = 1−y^4, x = 0; about x = 1.

**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

**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.

**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.

**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?