find the surface area of the portion of the surface z=4-x2/2 that lies above the region bounded by y=2x, y=0, and x=1

Q: Find the surface area generated by revolving the portion of the curve y=x^2+1 between x=1 and x=2…

A: Given that, Curve, y=x2+1   We have to find the Surface Area Generated by revolving the portion of…

Q: Find the surface area of revolution about the y-axis of y = 3 – 3x over the interval 0 < x <1

A: Given

Q: Find the volume of the solid obtained by rotating the region in The region  R  enclosed by the…

A: Given that, The curves are y = x and y = x2. (a) Volume rotation about the x-axis: Draw the given…

Q: Find the surface area of revolution about the x-axis of y = 3x + 4 over the interval 1 < x < 2

A: Answer

Q: b) Find the volume of the solid obtained by rotating the region bounded by the curve y = -x² + 11…

A:

Q: Calculate the area of the surface generated when the curve, y = Vx is revolved on the interval [1<…

A: y=x3then x=y3 area of the surface=∫12xddy=∫12y3dy=y4412

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A:

Q: Find the volume of the solid generated by rotating the region bounded by the curves y = e^x and y =…

A: In the question we have to find the volume of region bounded by the given curves.

Q: compute the surface area of revolution about the x-axis over the interval. y= x3, [0, 2]

A:

Q: Find the area of the plane region bounded by the curves y = Vx - 1, y = 3, the x-axis, and the…

A: Region bounded be the curves is given, we need to find the area of the region. Firstly,  we'll draw…

Q: Find the area of the surface obtained by rotating the curve about the y-axis. x=y^3, 0 less than or…

A: Consider the given curve and draw it,

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3x + 3y R:…

A:

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: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = 4x³.

A:

Q: The surface area of the surface generated by revolving y =x³ , 0 Sx<1 about the x- axis is

A: Given : y= x3    ,  limit  0 to 1

Q: Find the area of the surface generated by revolving the region bounded by, y6 1 x = + 16y4 i 1<ys 5…

A: In this question, we find the surface area generated by rotating the region bound by the given curve…

Q: (24) x+1 = y°, x= y,y = 0, y = 1

A:

Q: (b) Find the volume of the solid obtained by rotating the region bounded by the curve y=x²+x-2, y =…

A: Given is : The curves y=x2+x-2, y=0 The rotation is about the x-axis. We need to find the volume of…

Q: Find the surface area of revolution about the x-axis of y=4x+3 over the interval 0≤x≤1

A:

Q: Compute the surface area of the solid obtained by revolving the region between the x-axis and the…

A:

Q: Compute the surface area of revolution about the x-axis over the interval [0, n] for y = 6 sin(x).

A:

Q: Find the area of the surface generated by revolving the region bounded by, 1 1syss 16y4 y6 1<y< 5 6.…

A:

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

A:

Q: Find the surface area of revolution about the x-axis of y = 2x + 7 over the interval 0 <x <1

A:

Q: 5. Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 – x} about the x-axis.

A: Surface area

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = √(x2 + y2…

A: Given:The given function is f(x,y)=x2+y2and r=x,y: 0≤f(x,y0≤1To find:we have to find the area of the…

Q: Find the volume of the solid obtained when the region under the curve y = x/4 – x2 from x = 0 to x =…

A: Given data:     The given expression is: y=x(4-x2)1⁄2. The given limits of x is: (a,b)=(0,2). The…

Q: Find the surface area of the solid generated by revolving the region bounded by the graphs of y =…

A: We find dy/dx for y=x^2

Q: Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=6 about the…

A:

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

A:

Q: Find the volume of the solid that results when the region enclosed by the curves y = cos x and y =…

A:

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = 13 + x2 −…

A: Consider the provided functions, fx,y=13+x2-y2 And the region R=x,y: x2+y2≤4 Find the area of the…

Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the…

A:

Q: Find the area of the surface given by z = f(x, y)  that lies above the region R. f(x, y) = 13 + 9x…

A:

Q: Find the surface area of revolution about the x-axis of 5z +3 over the interval 1 < z < 2

A: y=5x+3 &amp; given interval 1≤x≤2As we know surface area of revolution abput x-axis from x=a to…

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A:

Q: b) Find the surface area of the region under the curve 2/3 2/3 =1 by revolving about x-axis. a

A: b We have to find the surface area of the the region under the curve xa23+ya23=1by revolving about…

Q: Find the surface area of the solid generated by revolving the region bounded by the graphs of y =…

A:

Q: Find the surface area of revolution about the x-axis of y=4x+1 over the interval 1≤x≤2

A: y=4x+1, 1≤x≤2 Differentiating with respect to x, we get dydx=41+0=4

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A:

Q: Find the surface area of revolution about the x-axis of y = 3x + 2 over the interval 0 < z <1

A:

Q: find the surface area of the surface f(x,y)=1/2x^2-y over the region bounded by the lines x=2, y=0…

A:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = x² + y2, R…

A:

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

A:

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = ln∣sec x∣…

A:

Q: Find the surface area of revolution about the x-axis of y 6x + 3 over the interval 2 < x < 5

A: In the question the curve given is - y=f(x)=6x+3 , 2≤x≤5 We need to find Surface area of revolution…

Q: Find the area of the surface given by z = f (x, y) that lies above the region R. f(x, y) = xy,  R =…

A: Consider the given: z=fx,yx2+y2≤16x2+y2≤42

Q: compute the surface area of revolution about the x-axis over the interval. y = (4 − x2/3)3/2, [0, 8]

A:

Q: Find the surface area of revolution about the y-axis of y = 5x + 1 over the interval 0 < x < 3

A:

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…

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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.