4. Find the volume of the solid generated by the curve f(x)=4-cos.x revolved 360° about the x- axis in the interval [0,2r].

Q: 1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and…

A: To find the volume of the prism described we just need to evaluate the given double integral…

Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A:

Q: O (y +ev* )dx + (2x + cos y)dy , where C is the boundary of the region enclosed by the parabolas y =…

A:

Q: The area of the surface generated by revolving the curve y=x² if 0<x<2 about the y-axis is given by…

A:

Q: 1 dA, where R is the union of both regions bounded by the functions y = sin(3x) x2 + y2 + 4 and y =…

A:

Q: 1. Find the area of the surface z = k + xy inside the cylinder x² + y² = R² for constant R. k > 0 is…

A:

Q: Consider the given closed rectangular box with dimensions x cm, v cm and z cm. Assume that x is…

A: Consider a rectangular box with dimensions x cm , y cm and z cm .…

Q: (9) Evaluate // 2² + y² + z²)³/? dV where D is the solid region in the first octant between the two…

A: Volume between the two spheres using spherical coordinates

Q: The volume of the solid generated by the curve y = e, between z = 2 and z = 6 about the z- azis is

A: Given: The curve is y=e-x   To determine: The volume of the solid generated by the curve y=e-x…

Q: check if it is homogeneous and to what degree (3x - cosy)dy t_x' dy =0

A: Find your answer below

Q: -x), with respect to OY. 4. The area bounded by the curve 2x+2x -y -2 0 and the line y=2x with…

A:

Q: 3. Evaluate // (22 + y) dV where G is the solid in the first octant bounded by r = y? and r+z = 1.

A:

Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

Q: 3 The triple integral L (x + 2y – z)dxdydz is equal to

A:

Q: If the curve y = ln x between x = 1 and x = e is rotated about the y-axis, which integral below…

A:

Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

A:

Q: Find the area of the surface formed by revolving the graph of f(x) = x3 on the interval [0, 1] about…

A:

Q: The dynamic equilibrium of a one-story building is described by the following equation: x(t) = xc(t)…

A:

Q: Evaluate the triple integral. xy sin y z dV, where G is the rectangular box defined by the…

A: We have to evaluate  the triple integral ∬∫GxysinyzdV Then,…

Q: 4. If the curve y = In x between x = 1 and x = e is rotated about the y axis, which integral below…

A:

Q: 2. Show that the surface area of the solid of revolution obtained by revolving the curve y = 1/x, x…

A:

Q: tind thie volume of thie solid gen. by rievolung Thie negion bounded by thie qivien linser k cune…

A: #1 Volume of the solid

Q: Q3/ Evaluate: 1- SS (4x + 2) for the region enclosed by the curves y = x² and y = 2x 2- Show that…

A: 1. Consider a function of two variables, z=fx,y. The double integral of function fx,y is denoted by…

Q: The double integral T f(x)g(y)dydx,where a,b.c, and d are constants, is equal to

A:

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 9y² + 9z2 and x…

A: Given the region

Q: 1) Evaluate the triple integral. | 6xy dV where E lies under the plane z = 1+x + y and above the…

A:

Q: Suppose f(x, y, z) = x² + y² + z? and W is the solid cylinder with height 9 and base radius 5 that…

A:

Q: The volume of the surface generated by rotating the function f(x) = (z (1 e 4) - %3D around the…

A: The volume of a solid can be obtained by integrating a small volume element within appropriate…

Q: Determine whether the following statements is true or false, and explain why.

A: Answer: False.

Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: 1š + z² + 2 f(z) = Calcule S f(x) dz.

A: Given data: The expression for the given function is f(x)=(x5+x2+2)/(x3-x). The integral of the…

Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

A:

Q: The surface area of the surface generated by revolving y= 1-x2 for 0<x<1 about the x - axis is S = […

A:

Q: te the triple integral x dV where E is the solid bounded by the paraboloid x = 9y + 9z? and x = 9. E…

A: Given query is to find value of the tripe integral.

Q: Find the surface area of the surface resulting from revolving the cu y=x+2 on the interval [0,1]…

A:

Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

Q: у 3 1 + sin х, 0 <x< т/2 y

A: The given curve is y=1+sinx and the limit is 0≤x≤π2 The Surface area is given by S=∫x2πy1+y'2dx or…

Q: The volume of the solid generated by the curve y = e², between z = 2 and z =7 about the I - azis is…

A: Given curve is y=e-x  x=2 and x=7 about the x axis find the volume

Q: The surface area of the surface generated by revolving y 1-x? for 0Sr<1 about the x-axis is S=…

A: Rule- If the curve y=f(x), a≤x≤b is rotated about the x−axis, then the surface area is given by

Q: 1 (#3) Find the surface area for y = 3 on [0, 3] rotating on the x- axis.

A: Given an equation of a curve, The solid will form by rotating the curve about the x-axis.

Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: A sphere of radius 2 cm contains a volume charge density Pv given by py = 4 cos“0 [C/m³]. Find the…

A: Given: Radius of the sphere=3 cm Charge density, ρv=4 cos2θ C/m3

Q: Approximate the integral fe* cos xdx using the composite Trapezoidal rule with M=5 subintervals. M-1…

A: The given integral is ∫01excos xdx. Approximate the integral ∫01excos xdx using the composite…

Q: Find a cubic approximation of r(θ) = (θ 2 , eθ , θ) at θ = 0.

A: given rθ=θ2,eθ,θ to find - cubic approximation at θ=0

Q: The double integral f(x)g(y)dydx ,where a,b.c, and C d are constants, is equal to

A:

Q: 4. Find the area of the surface formed by revolving the graph of f(x) = x² on the interval [0,…

A:

Q: The volume of the solid generated by the curve y = e¯ª, between x = 2 and x = 7 about the x – axis…

A: Given curve, y=e-x x=2  and   x=7

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

A:

Q: If we rotate the region under the curve y = 8 between x = 2 and x = 3 about the x-axis, what answer…

A: