3. Find a parameterization for the surface created by rotating the portion of y = x from x 1 to x = 2 around the y-axis. %3D %3D %3D

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

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = 2 6. 1 + 2x…

A: The surface is obtained by rotating the curve about x-axis.y=x36+12x, 12≤x≤1

Q: Find the area of the surface generated by revolving the curve about the (a) x-axis and (b) y-axis.…

A: Explanation and solution is given below....

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 4x = y? + 20,…

A:

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: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² -…

A: Above question is solved.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 5 + 3y, 1 <…

A: We have to find the surface area of the solid.

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: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V5 - x, 3 <…

A: Definition used -                             Area of the surface obtained by rotating the curve…

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

A: We need to find Surface area.

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. x -(y2 + 2)3/2,…

A:

Q: Find the exact area of the surface obtained by rotating the given curve about the y-axis. |x = 3t 0…

A:

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

A: Given  y =x3 ,  0 ≤ x ≤2The area under a curve is the area between a curve f(x)and the x-axis on an…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V8 - x, 25…

A: given, y=8-x  ,2≤x≤8  the graph is

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 1 y = + /- 2x

A: Given: The equation of the curve y=x36+12x,where  12≤x≤1. Calculation: Compute the surface area as…

Q: Find the exact area of the surface obtained by rotating the given curve about the y-axis.

A: Given that      x(t)=3t-t3y(t)=3t2 Since, we are rotating about y-axis, the formula is:…

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: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + ex,…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V6 - x,…

A:

Q: 3) Find the area of the surface obtained by rotating the given curve about the indicated line, y=x2,…

A:

Q: Find

A:

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

A: Given function is x=13y2+22 and 3≤y≤4 We have to find the exact area of the surface obtained by…

Q: Find the exact area of the surface obtained by rotating the curve about the y- axis: y = 3 + 5x?,…

A: Consider the given function and interval. y=3+5x2, 3≤x≤8 If y=f(x) is function and the interval of y…

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

A:

Q: Find the exact area of the surface obtained by rotating the curve x = (1/3)y^3, 0 &lt;= y &lt;= 1,…

A:

Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. 9x =y2 + 18 ,  2…

A: Consider the curves, 9x=y2+18,  2≤x≤6 Differentiate the given curve with respect to “y” then,…

Q: 1.a)Find the area of the surface generated by revolving the curve y=√(121-x^2), −1 ≤ x ≤ 1 about the…

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Q: 4. Find the area of the surface generated when the given curve is revolved about the y-axis. y=(2x)"…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 4. Find the area of the surface obtained by rotating the curve y? = x + 1, 0<x < 3. about the x-axis…

A:

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

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = 1 1sxs1 2x'…

A: The given curve is  y=x36+12x

Q: 5. Find the exact area of the surface generated by revolving the given curve about the y- axis, Draw…

A: Application of integration

Q: Example Find the exact area of the surface obtained by rotating the curve y? = x + 1, 0 <x< 3, about…

A:

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

A:

Q: Let C be the curve y =x3/2, 1 < x < 4. (a) Find the length of this curve. (b) Find the surface area…

A: Given curve is

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

A:

Q: 6. Find the exact area of the surface obtained by rotating the curve, y = x³, 0 < x < 2, about the…

A:

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 2(x² −…

A:

Q: Find the exact area of the surface obtained by rotating the curve x = 1/3y3, 0 &lt;= y &lt;= 1,…

A: For rotation about y-axis, the surface area of the curve is given by

Q: Find the exact area of the surface obtained by rotatingthe curve about the x-axis. y =√(1+ 4x)  ,  1…

A: Find the exact area of the surface obtained by rotatingthe curve about the x-axis.

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

A: Given curve is  y=x36+12x Differentiate with respect to x. dydx=x22-12x2

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + 5x, 1<…

A:

Q: Find the exact grea of the surface obtained by rotating the curve about the X-axis y= x', OSXSI

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = V1 + e*, 0 <…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x, 0< x< 5

A: Surface area of given curve after rotation about x axis.

Q: 15) Consider curve C which is the intersection of the surfaces shown in the attached figure. The…

A: The equation of the graphs given are as follows: x=-34y2+3y=yz=y22 We are asked to evaluate the…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. (y2 + 2)3/2, 2 <…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. < =v² + 2)3/2, 3…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.