Find the areas of the surfaces generated by revolving the curves in Exercises 1-14 about the axes indicated. 1. y = x/2,0sxS4, about thex-axis. Check your result with a formula from geometry, as in Example 2. 2. y = x/2,0sxS4, about the y-axis. Check your result with a formula from geometry, as in Example 2. 3. y = (x/2) + (1/2), 1SxS3, about the x-axis. Check your result with the geometry formula in Eq. (1).

Find the areas of the surfaces generated by revolving the curves in Exercises 1-14 about the axes indicated. 1. y = x/2,0sxS4, about thex-axis. Check your result with a formula from geometry, as in Example 2. 2. y = x/2,0sxS4, about the y-axis. Check your result with a formula from geometry, as in Example 2. 3. y = (x/2) + (1/2), 1SxS3, about the x-axis. Check your result with the geometry formula in Eq. (1).

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter9: Surfaces And Solids

Section9.CT: Test

Problem 8CT: Determine whether the statement is true or false. a A right circular cone has exactly two bases. b...

See similar textbooks

Related questions

Q: 5- Finding the areas of the surfaces generated by revolving the curves in exercises about the…

Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

Q: 13. Find the area of the surface generated when the curve y = -, on [2,4] is rotated about the…

Q: a. Find the area of the surface generated by revolving about the x-axis the loop of the

Q: Find the areas of the surfaces generated by revolving the curves in Exercises 31–32 about the…

A: 31.The functions are,

Q: 4: Show yor work. a) 1: Find the exact area of the surface obtained by rotating the curve y? +x =5,…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 5- Finding the areas of the surfaces generated by revolving the curves in exercises about the…

A: Surface of revolution of a curve about a line is the surface generated by revolving the cure about…

Q: 11. Find the area of the surface obtained by rotating the curve y = a, 0 < a < 3/4, about the a…

A: Surface area of revolution

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 2 + 2)3/2, 1s ys…

A: The curve x=13y2+232 revolved about x-axis on 1≤y≤4

Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

Q: 3. (8.3) find the area of the surface obtained by rotating the curve y = v4- x2, -1<x < I about the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3 ( y2…

A: Given curve is x=13y2+232 over 1 ≤ y ≤ 2. The exact area of the surface obtained by rotating the…

Q: 5. Find areas of the surfaces generated by revolving the curves about the indicated axes x =t+V2…

Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

Q: Find the area of the surface generated by revolving the curve y = / 2x - x , 0.75<x<1.75, about the…

Q: Determine the points on the surface y2 + z2 − x = 8 that are closest to the origin. Solve problem…

Q: 3. Find the area of the surface generated by revolving the curve y = 2/x ,1Sx<2, about the x-axis(as…

Q: 1. a) Find the length of the curve: y=+[1,2]. b) Find the area of the surface obtained by rotating…

Q: Solve for the surface area of a plane curve rotated about y-axis. y = ((x^6)/12)+(1/(8x^4)), 1 ≤ x…

Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

Q: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

Q: Identify a generating curve on the xz-plane for the surface of revolution with equation x2 + y? + 22…

A: Solution :-

Q: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3, 0 ≤…

A: We have to find the area of surface.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3 4 + 1…

A: Sarface area problem....

Q: In exercises 13-18, compute the surface area of the surface obtained by revolving the given curve…

A: Solving part (b) as requested. Given:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1/3(y2 +…

Q: Write the equation x +z* - (y- 1) = 0 in cylindrical sy stem. W hich surface does it represent? Give…

A: Given : The equation x2 + z2 - (y - 1)2 = 0 To write the given equation in…

Q: 5. Find the exact area of the surface obtained by rotating the curve y = V16 x2, -2<*<2 about the…

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

Q: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

Q: (a) Find the area of the surface generated by the given curve about x-axis y = V, (b) Find the area…

Q: 3- Find the surface area of the solid obtained by rotating the curve z= 2/4- y; 0Sysabout the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = square…

A: This is a problem related to find area of the curve using integration. Please use below method to…

Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

Q: i) Find the exact length of the curve y X y = 2 X + — ii) Find the exact area of the surface…

A: Let's find exact length and area of surface.

Q: 2 Find the area of the ellipse cut from the plane z = 3x by the cylinder x² + y² = 16. Surface area…

A: Given plane z=3x and the cylinder x2+y2=16. The objective is to find the area of the ellipse cut…

Q: 13. Find the area of the surface generated when the curve = , on [2,4] is rotated about the y-axis.

A: The solution are next step is

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

Q: 5- Finding the areas of the surfaces generated by revolving the curves in exercises about the…

Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

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

A: y2=12x ⇒y=23x ⇒dydx=3x ⇒dydx2=3x2 ⇒dydx2=3x ⇒1+dydx2=1+3x ⇒1+dydx2=1+3x

Q: Give an equation of the surface of revolution generated by revolving x In z about the z-axis.

Q: Find the area of the surface obtained by rotating the curve about the x-axis. X 름-빨 In x Select the…

A: The given problem is to find the area of surface obtained by rotating the given curve about the…

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

Q: Find the surface area of the solid of revolution obtained by rotating the the curve about the…

A: start with:

Q: ii) Find the exact area of the surface obtained by rotating the curve 1 12x 3 y = x³ + 9 1 ≤ x ≤ 2,

Q: The exact area of the surface obtained by rotating the following curve 6x = y + 12, 2 < x < 3 about…

Question

Find the areas of the surfaces generated by revolving the
curves in Exercises 1-14 about the axes indicated.
1. y = x/2,0 sx<4, about the x-axis. Check your result
with a formula from geometry, as in Example 2.
2. y = x/2, 0sxS 4, about the y-axis. Check your result
with a formula from geometry, as in Example 2.
3. y = (x/2) + (1/2), 1S*S3, about the x-axis. Check
your result with the geometry formula in Eq. (1).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Double Integration$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Elementary Geometry For College Students, 7e

Geometry

ISBN:

9781337614085

Author:

Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,