Find the area of the surface generated by revolving the curve x =.30sy<2, about the y-axis.2

Given: The curve is x=y32, 0≤y≤2 about the y-axis The formula for find the area of the surface is…

Answered: Find the area of the surface generated…

Math

Calculus

Find the area of the surface generated by revolving the curve x = Osys2, about the y-axis

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

See similar textbooks

Related questions

Q: Find the area of the surface generated by revolving x= 4/9 - y,0sys about the y-axis. 16 x=49-v 12

Q: 10 Find the area of the surface generated by revolving the region bounded by. ISKSS about the…

Q: Use a computer algebra system to find the approximate surface area of the solid generated by…

A: To find the surface area using the computer algebra sysytem

Q: Find the volumMe generated by revolving the area bounded by the giveN Curve and avd lines y = x', x…

Q: 2. Find the surface area generated by revolving the circle x = cost, y = 1 + sint, 0sts2n over x -…

A: Use formula of area about x axis

Q: Find the surface area of revolution about the x-axis of R.

A: Given curve y=2x, 2.3≤x≤4.2 We have to find the surface area of revolution.

Q: Find the area of the surface generated by revolving the curve x = Vy, 0<y <4, about the y-axis.

A: We will use standard method.

Q: Compute the surface area formed by rotating the portion of the curve in the first quadrant about the…

A: Given curve is x=(cost)(1+cost),y=(sint)(1+cost) , 0≤t≤2π Differentiate with respect to t.…

Q: The area of the region bounded by the two curves y=z' and y 64 is %3D Square Units

Q: Find the lateral surface area of the cone generated by revolving the line segment y = x/6, 0 sx s2…

Q: Find the surface area generated by revolving x=sqrt(8y-y^2) about the y axis on the interval: y=…

Q: Determine the moment of inertia of the area bound by the two curves about the x and y axis. y y = x?…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: Find the area of the surface obtained by rotating the region y = x°, 0<x < 3 about the x-axis.

Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

Q: y = } + sxs1 <x<1 2

Q: Find the surface area of revolution of x=y2 about the y-axis at [0,2]. Graph.

Q: find the area of surface of revolution generated by revolving about the x-axis the arc y…

Q: Find the surface area of revolution about the y-axis of y VOur ancwor in torme of round to docimal…

Q: Find the area of the surface generated by revolving the curve about the indicated axis. 36) y=V4x -…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: iii) Set up an integral for the area of the surface generated by rotating the curve about the…

Q: Find the area of the surface generated by revolving the region bounded by, 1 1sx55 8x2 about the y-…

Q: Determine the area of the surface generated by revolving y=x³ on (0,1), about the x-axis.

A: The given curve is y=x3 on 0, 1 about x-axis. This implies that,…

Q: Find the area of the surface generated by revolving the curve about the indicated axis. SET UP ONLY…

A: The area of the surface generated by revolving the curve around the y axis can be given as:…

Q: Sketch the region enclosed by the curves and find its area. 1 Y = V1 – 9x2' y = 2

Q: Find the area of the surface obtained by rotating the curve y = V1+ e, 0sx<1 about the X-axis. 2).…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 40,0 ≤ 0 ≤…

Q: Find the area of the surface generated by revolving x = 6t and y = 4ť (0 < t < 1) X

A: answer is in next step

Q: Find the surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

Q: Find the area of the surface generated by revolving the given curve about the yy-axis.…

A: Given curve is, x=25-y, -1≤y≤0 Now, differentiating with respect to y we get,…

Q: Find the area of the surface that is obtained by rotating the graph of X = 1+ Y² (Y = 1 to Y= 2)…

Q: Find the area of the surface obtained by rotating the curve about the x-axis. y= e*, 0sxs1 Set up…

Q: Find the area of the surface obtained by rotating the curve. y=x+, 1<x< 2 rotated about the x-axis…

Q: Find the area of the surface generated by revolving the curve y = 3sqrt(x) between x = 0 and x = 4…

A: Given curve, y=3x x = 0 and x = 4

Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y. Determine the derivative dxdy=12y The formula for the area of surface…

Q: Find the moment of inertia with respect to the y-axis of the area bounded by the curve y=1-x3 and…

Q: find the surface area by rotating the curve about the y-axis; y=x^3 from x=0 to x=2

Q: Find the area of the surface generated by revolving the region bounded by, 1sx55 8x2 about the y -…

Q: Find the area of the surface generated when the given curve is revolved about the given axis. 3 7 y…

A: We write x in terms of y first

Q: Find the area of the surface obtained by rotating the curve y = x² - In(x) about the y-axis for 3…

Q: Find the surface area generated by revolving about the x-axis the curve y = 2(15-x)^1/2, from x =…

Q: D Find the area of the surface generated by revolving the region bounded by, 1 1 <x < 5 4 8x2 about…

A: In the question we have to find area of the given function.

Q: Find the area of the surface obtained by rotating the curve y = about y-axis for 1 ≤ y ≤ 3. Area:

Q: Find the area of the surface that is obtained by rotating the graph of X = 1+Y² (Y = 1 to Y= 2)…

Q: Find the surface area obtained by rotating y = V9 – x² -2sxs-1

A: As we know that; The expression for the area of surface rotating about the x-axis. S=2π∫abfxf'x2+1dx…

Q: Find the surface area generated by revolving the parabolic arc y=x² , Osxs6 around y-axis

Q: Find the surface area of the curve f (x) = x over [1,2| rotated .3 3 about the – axis -

A: The revolution of the curve y = f(x) around the x-axis is: S=2π∫abf(x)(f'(x))2+1dx

Q: Find the surface area generated by revolving about the x-axis the curve y = 2(15-x)^1/2, from x =…

Q: Find the volume and the surface area that generated due to rotate the bounded area between the curve…

A: I use washer method to find volume about x axis

Q: Find the surface area generated by rotating y=(1/3)x^3 bounded by y=0 , x=0 , and x=9 about the the…

Question

Find the area of the surface generated by revolving the curve x =
.3
0sy<2, about the y-axis.
2

Expert Solution

Step 1

Given: The curve is $x = \frac{y^{3}}{2}$ , $0 \leq y \leq 2$ about the y-axis

The formula for find the area of the surface is $S = 2 π \int_{a}^{b} x \sqrt{1 + {(f' (y))}^{2}} dy$

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here