
Find the area of the surface generated when y=4x and x=1 is revolved about the yaxis.

Find the area of the surface generated when y=4x and x=1 is revolved about the yaxis. We have to use the surface area formula of revolution. Integral (2pi*f(x)sqrt(1+f'(x)^2))dx

Find the area of the surface generated when y=4x and x=1 is revolved about the yaxis. We have to use the surface area formula.

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. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with

There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region R is bounded by the


The region R is bounded by the xaxis, x = 1, x = 3, and y = 1/x3. a.) Find the area of R. b.) Find the value of h, such that the vertical line x = h divides the region R into two Regions of equal area. c.) Find the volume of the solid generated when R is

The region R is bounded by the xaxis, x = 1, x = 3, and y = 1/x^3. a.) Find the area of R. b.) Find the value of h, such that the vertical line x = h divides the region R into two Regions of equal area. c.) Find the volume of the solid generated when R is

1. Let R be the region bounded by the xaxis, the graph of y=sqr(x) , and the line x=4 . a. Find the area of the region R. b. Find the value of h such that the vertical line x = h divides the region R into two regions of equal area. c. Find the volume of

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. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with

Suppose that the region between the xaxis and the curve y=e^x for x>=0 has been revolved around the xaxis. Find the surface area of the solid. I got 3*pi The book shows an answer of pi * [sqrt(2) + ln(1 + sqrt(2))] Where do I go wrong? For the sides of

The curve y=sinh(x),0

The region R is bounded by the xaxis, x = 1, x = 3, and y = 1/x^3. C. Find the volume of the solid generated when R is revolved about the xaxis.

Let R be the region bounded by the xaxis and the graph of y=6xx^2 Find the volume of the solid generated when R is revolved around the yaxis

find the volume generated by the boundaries y=x^3+1 , xaxis , x=1 , x=2 revolved about yaxis

Find the surface area of the solid generated by rotating the area between the yaxis, (x^2/y) + y = 1, and 1≤y≤0 is rotated around the yaxis.


Region R is bounded by x=22y^2 and x=1y^2 find the volume of the solid generated if R is revolved about the yaxis Anybody help me with this? thanks!

Let 𝑆 be the region (in the first quadrant) bounded by a circle 𝑥^2 + 𝑦^2 = 2, 𝑦^2 = 𝑥 and the 𝑥axis (ii) Find the volume of the solid generated by rotating the region 𝑆 about the 𝑦axis (c) Find the surface area of the solid

Find the surface area generated when y = (x^3/12) + (1/x), from x=1 to x=2 is rotated around the xaxis.

Use the disk method to find the volume of the solid generated when the region bounded by y=15sinx and y=0, for 0

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 xy =2

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=4x^2

if the region enclosed by the yaxis, the line y=2 and the curve y=the square root of x is revolved about the yaxis, the volume of the solid generated is????

Find the area of the surface generated by revolving the curve y = (x + 3)^1/2, 2 ≤ x ≤ 4 about the xaxis.

Find the volume of the solid generated by revolving the region bounded by y=x+(x/4), the xaxis, and the lines x=1 and x=3 about the yaxis. I've drawn the graph and I understand which part is being rotated, but I'm having trouble setting up the equation.

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. Find the volume of the solid generated when R is revolved around the line y=pi. B. Fine the volume


Find the area of the surface generated by revolving the given curve about the yaxis. 8xy^2=2y^6+1 , 1

Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes. x = y  y3, x = 1, y = 1 (b) Revolved about the yaxis ? Hi Shawn, 97/105 * pi ? :) We need to cut away the volume of the

The graph of the curve y2=10 x+10 is a parabola, symmetric with respect to the xaxis. Find the area of the surface generated by rotating about the xaxis the part of this curve corresponding to 0 ≤ x ≤ 20.

I am in Calculus and am currently learning how to find the Area of a Surface of Revolution. I cannot understand what the surface of revolution (whether it's the xaxis, yaxis, or y=6) is. For example, I had a problem saying to use the washer method to

find the area of the surface generated by revolving about xaxis the upper half of the ellipse 4x^2 + 16y^2 = 64

Find the volume when the area bounded by f(x) = xe^x, y = e, and the yaxis, is revolved around the yaxis.

Find the volume when the plane area bounded by y=x^23x+6 and x+y3=0 is revolved about (1) x=3 and (2) about y=o B. Find the volu6 of focus generated by revolving the circule x^2+y^2=4 about the line x=3

Set up (do not evaluate) the integral that gives the surface area of the surface generated by rotating the curve y=tanhx on the interval (0, 1) around the xaxis. Anyone who can help? Not really sure how to even begin! Thanks

Given the area is in the first quadrant bounded by y²=x, the line x=4 and the 0X What is the volume generated when this area is revolved about the 0X? the answer is 25.13 but I don't know how. help me please

This is the questions I have trouble with : Set up (do not evaluate) the integral that gives the surface area of the surface generated by rotating the curve y=tanhx on the interval (0, 1) around the xaxis. Anyone who can help? Not really sure how to even


find the volume generated of the region bounded by the parabola y=x^2 and the line y=b when revolved (b>0): a.) about the xaxis b.) about the line y=1 c.) about the line y=a, where a>b

2. Let R be the region of the first quadrant bounded by the xaxis and the cuve y=2XX^2 a. Find the volume produced when R is revolved around the xaxis b. Find the volume produced when R is revolved around the yaxis

Find a definite integral indicating the area of the surface generated by revolving the curve y = 3√3x ; 0 ≤ y ≤ 4 about the x – axis. But do not evaluate the integral.

The region R is bounded by the xaxis, yaxis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the xaxis. C. The solid formed in part B is divided into two solids of

The region R is bounded by the xaxis, yaxis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the xaxis. C. The solid formed in part B is divided into two solids of

Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the xaxis. y = (x³/6) + (1/2x), 1≤ x ≤ 2

The region enclosed by the graph of y = x^2 , the line x = 2, and the xaxis is revolved abut the yaxis. The volume of the solid generated is: A. 8pi B. 32pi/5 C. 16pi/3 D. 4pi 5. 8pi/3 I solved for x as √y and set up this integral: 2pi * integral from

The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the xaxis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I drew it out on a graph

The region enclosed by the graph e^(x/2), y=1, and x=ln(3) is revolved around the xaxis. Find the volume of the solid generated. I don't understand if we have to use the washer method or the disk method for this one because when I drew it out on a graph

Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the yaxis. y = cube rt. (x) + 2 Thank you so much!!


Find the volume generated by rotating the area between y = cos( 3 x ) and the x axis from x = 0 to x = π/ 12 around the x axis

find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the yaxis.

find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the yaxis

Consider the graph of y^2 = x(4x)^2 (see link). Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the xaxis, (b) the yaxis, and (c) the line x = 4. goo.gl/photos/v5qJLDztqsZpHR9d7 I'm just having trouble

The region A is bounded by the curve y=x^25x+6 and the line y = x + 3. (a) Sketch the line and the curve on the same set of axes. (b) Find the area of A. (c) The part of A above the xaxis is rotated through 360degree about the xaxis. Find the volume of

Hello. I would appreciate it if someone could check my answers. I'm sorry it is so long. 1.) Let R denote the region between the curves y=x^1 and y=x^2 over the interval 1

A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the xaxis from 4 to 9. For part B of our question , the surface

The area bounded by the curve y^2 = 12x and the line x=3 is revolved about the line x=3. What is the volume generated?

Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=1 about the axis. about the xaxis. surface area= ⌠ 2pi * f(x)*sqrt[1 + (f'(x))^2] dx from a to b ⌡ it's been 45 years since I used that formula. I ended up with the

let R be the region of the first quadrant bounded by the xaxis and the curve y=2xx^2. Find the volume produced when R is revolved around the Xaxis


The region in the first quadrant bounded by the 𝑦axis and the curve 𝑥 = 2𝑦2 − 𝑦3 (graph please) is revolved about the 𝑥axis. Find the volume?

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.

This is a question from my textbook that does't have a solution and quite frankly I have no idea what to do. Any tips would be greatly appreciated. Given the function f defined by f(x) = 9  x^2. Find the surface area bounded by the curve y = f(x), the x

The region enclosed by the curve y =e^x, the xaxis, and the lines x=0 and x=1 is revolved about the xaxis. Find the volume of the resulting solid formed.

The region enclosed by the curve y = ex, the xaxis, and the lines x = 0 and x = 1 is revolved about the xaxis. Find the volume of the resulting solid formed. How do you do this?

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.

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.

The following are about an infinite region in the 1st quadrant between y=e^x and the xaxis. A) Find the area of the region B)Find the volume of the solid generated by revolving the region about the yaxis

Find the volume generated if the region bounded by y = sin 2x and y = cos x, π/6 ≤ x ≤ π/2 is revolved about the line y = 2. Use the method of washers.

Find the volume of the solid generated by rotating the area bounded by y=x^2 and x=y^2 about the xaxis.


Find the volume of the solid generated by rotating the area bounded by y=x^2 and x=y^2 about the xaxis.

Let R be the region bounded by the yaxis 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 xaxis. Find the exact volume of the solid.

Let R be the region bounded by the yaxis 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 xaxis. Find the exact volume of the solid.

the region bounded by the graph f(x)=x(2x) and the x axis is revolved about the y axis. Find the volume of the solid. I did the integral using the shell method, but the answer wasn't correct.

Find the area of the surface of revolution generated by revolving the curve y = 3 sqrt (x), 0

Find the volume generated when the area bounded by the curve y^2 = 16x, from x = 0 to x = 4 is rotated around the xaxis.

Region R is bounded by the functions f(x) = 2(x4) + pi, g(x) = cos^1(x/2  3), and the x axis. a. What is the area of the region R? b. Find the volume of the solid generated when region R is rotated about the x axis. c. Find all values c for f(x) and

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 xaxis, and on the right by the yaxis, about the line x = 1 I have gathered, that

Find the volume of the solid generated by rotating about the y axis the area in the first quadrant bounded by the following curve and lines. y=x^2, x=0, y=2.

Find the volume generated by rotating about the x axis the area bounded by x=0, y=2sinxcosx,, y=2cosx, and x=4, if 0≤x≤pi/2. I don't get the graph.


Use the cylindrical shell method to find the volume of the solid generated by revolving the area bounded by the given curves (x3)^2 + y^2 = 9, about yaxis.

Let S be a region bounded by the curve y=x+cosx and the line y=x as shown in the given figure. Find the volume of the solid generated when S is rotated about the xaxis. Find the volume of the solid generated when S is rotated about the yaxis.

Consider the graph of y2 = x(4 − x)2 (see figure). Find the volumes of the solids that are generated when the loop of this graph is revolved about each of the following

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.

Volume of the area bounded by y=sin(x), xaxis, x is greater than or equal to 0 but less than or equal to pi, revolved about x=3pi/2.

This is another textbook number that doesn't have the solution and I can't figure it out. Any tips would be greatly appreciated. For each of the plane surfaces, calculate the exact surface area. (Answer in fractions) (a)The surface composed of all surfaces

Let A be the region bounded by the curves y=x^26x+8 and y=0, find the volume when A is revolved around the xaxis

Find the volume of the solid bounded by the curves y = 4  x^2 and y = x revolved about the x axis.

A.Find the area of the region bounded above by y=2cosx and above by y=secx,π/4≤x≤π/4. B.Find the volume of the sold generated by revolving the region in (A) above about the xaxis

A rectangular strip 25cm*7cm is rotated about the longer side. find the total surface area of the solid thus generated.


I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 and y = 2x^2 about the

The region bounded by y= 1/(x^2+2x+5), y=0, x=0, and x=1, is revolved about the xaxis. Find the volume of the resulting solid.

Let A be the region bounded by the curves y = x^26x + 8 and y = 0. Find the volume obtained when A is revolved around the YAXIS

Find the volume of the solid formed when the region bounded by y=3x^2 and y=36x^2 is revolved about the xaxis.

Find the volume of the solid that is obtained when the region under the curve y = 4 − x^2/6 is revolved around the y axis between y = 0 and y = 4 .

The region bounded by y=e^(x^2),y=0 ,x=0 ,x=1 and is revolved about the yaxis. Find the volume of the resulting solid.

Let A be the region bounded by the curves y = x^26x + 8 and y = 0. Find the volume obtained when A is revolved around the YAXIS

Find the volume of the solid that is obtained when the region under the curve y=©ø¡îx+3 over the interval [5, 24] is revolved about xaxis.

Why isn't the surface area of a sphere with radius r the following: 2*pi * (pi*r) That comes from the following flow of logic: Doesn't it makes sense to think of the surface area of the sphere with radius r as the the circumference of the semicircle with

the region in the first quadrant bound by the graphs y=(x*x*x)/3 and y=2x is revolved about the yaxis. find the volume of the resulting solid.


Use cylindrical shells to find the vol of the solid that results when the region enclosed by y=x^35x^2+6x over [0,2] is revolved about the y axis

Use cylindrical shells to find the vol of the solid that results when the region enclosed by y=x^2, y=4 and x=0 is revolved about the x axis

5. Find the volume of the solid generated by revolving the region bounded by y = x2, y = 0 and x = 1 about (a) the xaxis (b) the yaxis

Find the volume of the solid generated by revolving the triangular region with vertices (1,1), (b,1), and (1,h) about: a) the xaxis b) the yaxis

Find the volume of the solid generated by the region in the first quadrant bounded above by the 3x+y=6, below by the xaxis, and on the left by the yaxis, about the line x= 2.