ii) Find the area of the surface obtained by rotating the curve y = e-, -1

Q: A hole is drilled through the center of a sphere x²+y² +z? = R,², leaving a ring-shape solid. If the…

A:

Q: 2. Use Green's Theorem (and only Green's Theorem) to evaluate |(2? + y)dx + (x² – y³)dy, where C is…

A:

Q: Find the surface area of the part of a sphere having radius 2 centered at origin for 1 <z < 2. 8pi O…

A: Given  Radius of the sphere R=2 and 1&lt;z&lt;2

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: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: 35. Find the area of the surface generated by revolving the para- metric curve x = 1, y = 21² (0 ≤1…

A: Given parametric curve is , x=t, y=2t2 ( 0≤t≤1 ) So, the required area of the surface generated by…

Q: Compute the area of the portion of the cone x2 +y = z2 with z z 0 that is inside the sphere x y z…

A: Given the area of the cone is x2+y2 = z2 and the sphere is x2+y2+z2 = 2Rz.

Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Surface are of the surface z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the projection of the…

Q: The sphere of radius a centered at the origin is expressed in Cartesan coordinate as x +y² +z? = a².…

A:

Q: For an area A in the x-y plane, in the expression I₂ = Ix+ly, the term /₂ is the: Minimum…

A: Introduction : As per definition, The polar amount of inertia is the total sum of the moment of…

Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

A:

Q: Show that the surface area of a sphere with radius a equals 4ra². r(u, v)= (a sin u cos v, a sin u…

A:

Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

A:

Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: 21 Verify Green's theorem in the plane for the integral ${(x-y) dx- (+xy) dy} | where c is the…

A: Green's theorem for a plane states that if C is a closed curve inclosing a region D and u and v are…

Q: 2. (a) Find the exact surface area that is generated by revolving the portion of the curve y = x²…

A: Given A surface area that is generated by revolving the portion of the curve y = x2 between x = 2…

Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: Surface at 0 = 30° and r = 10 is a.. Cylinder Cone Circle Plane

A: Solve

Q: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of…

A: Given: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis.

Q: A hole is drilled through the center of a sphere x +y +z? = R,', leaving a ring-shape solid. If the…

A:

Q: Find the surface area of a sphere with radius, r=8 in. S.A. = in (Type an exact answer in terms of…

A:

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

A:

Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…

A: Given That  ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate  ∬Curl F →·dS→  using strokes theorem

Q: The figure shows the surface created when the cylinder y2 + z2 =1 intersects the cylinder x2 + z2 =…

A: It is given that, the cylinder y2 + z2 =1............... (1) intersects the cylinder x2 + z2 = 1…

Q: Which one, y=ex, 1≤y≤2, gives the surface area of the solid formed by rotating the curve segment…

A:

Q: 10. Find a parameterization for the part of the plane x + 2y +z = 6 in the first octant. Compute the…

A:

Q: The volume of the solid that lies above the cone θ=π4 and below the sphere r=cos(θ) is: (Here,…

A:

Q: Find the surface area of the cone frustum generated by revolving the line segment y-/2) + (1/2, 1…

A:

Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

A:

Q: Use triple iutegral in reitanqular coordinates +to tindd te nass of. sphere with den a ensing S こス…

A: mass = density * volumem        = massδ         = densityV        =…

Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: Consider the plane region bounded by the graphs of y = k, y = 0, x = 0, and x = b, where k &gt; 0…

A: Given: The plane region is bounded by the graphs given as follows, The plane is drawn for the given…

Q: 1- Find Aue Volume the Paralle RPed by usi+j-21k and V= -i_-k ,W = 2i44j-2K %3D

A: As we know that the volume of the parallelepiped is: V=u→·v→×w→ Given:…

Q: The arc of the parabola y = x? from (1, 1) to (2, 4) is rotated about the y-axis. Draw the surface…

A: Given: Equation of parabola : y= x2  Arc of parabola passes through (1,1) and (2,4).

Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

A:

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

A:

Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: 7. Find the surface area of the cone frustum generated by revolving the line segment x 1 y ==+ 1s…

A:

Q: 2 What Is the equatlon of the clrcle with a radius of 5 and center at (2, 3)? F (x + 2)2 + (y + 3)2…

A:

Q: 6) 3 =x2 porobola, find the yolume of the object by notating +his porabola ond the regjen around the…

A:

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

A:

Q: The curre y=J36 - z' , -4£ x s4 will be rotated about the ルーaXis. find the area that results af the…

A:

Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: A hole is drilled through the center of a sphere x2 + y? +z? = R², leaving a ring-shape solid. If…

A:

Q: 4) The area of the surface generated by revolving x=y²-1, 1≤ y≤ 2 about x-axis is S=.

A:

Q: Q#4 a. Find the area of the surface generated by revolving abuut the x – uxis the portion of the…

A:

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

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.