64. Verify Stokes' theorem for F = xz i – yj +x?y k, where S is the surface of the region bounded by x= 0, y = 0, z = 0, 2x +y +2z = 8 which is not included in the xz plane. %3D Ans. common value = 32/3

Q: Sketch the region enclosed by the given curves. y = 6 cos ax, y= 12x² – 3 y y 4| 2 -1.0 -05 d.5 1.0…

A: Area of the Region bounded by the curve :     If f(x) and g(x) are two continuous function on [a,b]…

Q: 30 Find the volume of the solid generated by rotating the region bounded by the curve y=(x-2) and…

A:

Q: Evaluate the surface integral. xz dS S is the boundary of the region enclosed by the cylinder y2 +…

A: S is composed of three boundary surfaces:            S1:y2+z2=49S2:x=0S3:x+y=10 For S1, The…

Q: Use Green's Theorem to evaluate the line integral. y? dx + xy dy C: boundary of the region lying…

A: From Green's theorem, ∫CMdx+Ndy=∬∂N∂x-∂M∂ydydx If M=y2 ;N=xy, then ∂N∂x=y ; ∂M∂y=2y

Q: Consider the curves y = a + 1, y = 2, and a = 0. Set up the integrals for the following. The volume…

A:

Q: A region R is bounded by the graphs of  y=0.8 (x)^1/2 and y=0.8x.  Find the moments Mx and My of R…

A: Given,

Q: Sketch the region R whose area is given by the iterated integral. *16 – y² dx dy 14 12 10- y 8. 4 2-…

A: Solve by using graph

Q: b) [ Find the volume of the solid obtained by rotating the region bounded by the curve about the…

A:

Q: d the volume V of the solid obtained by rotating the region bounded by the ren curves about the…

A:

Q: Find the volume.

A: Find the region R in the x-y plane.The x-axis is y = 0 and y axis is x = 0 line.R is the region…

Q: Consider the path integral (x + 2y)dx + (3x – 4y)dy, where C is the path formed by the y axis, the…

A:

Q: Set up the integral in polar coordinates to find the mass of the lamina bounded by the y-axis, y= x,…

A:

Q: Express the double integral || (x+1)dA, where N is the region in the upper plane (i.e. y2 0) between…

A: The integral is,∫∫Ωx+1dA, where Ω is the region in the upper half plane  between x2+y2=4 and x2+y2=9

Q: - Find the volume of the solid generated by revolving about the line x = 1 the region bounded by the…

A:

Q: -: Let R be the region in the plane bounded by the lines y=x, y=1 and x=0. The area of the region R.…

A: R be the region in the plane bounded by the lines y = x, y = 1, and x = 0. The area of the region is…

Q: 1. Use the change of variables = u? - v², y = 2uv to evaluate the integralS Se ydA, where R is the…

A:

Q: Use Green's Theorem to evaluate the line integral. | y? dx + xy dy C: boundary of the region lying…

A:

Q: The volume of the solid generated by revolving the region between the parabola x =y2+1 and the line…

A: Given that: x=y2+1and line x=10about the line x=10

Q: 11. xyz dV, where G is the solid in the first octant that is bounded by the parabolic cylinder z = 2…

A: To evaluate the triple integral

Q: Find the area of the surface given by z = f(x, y) over the region f(x, y) = In(|sec(x)|) %3D ={(x,…

A:

Q: Evaluate ([ [xz? dy dz + (x²y – z) dz dx + (2xy + y²z) dx dy], where S is the surface enclosing a…

A: 3. Given integral is ∬sxz2dydz+(x2y-z3)dzdx+(2xy+y2z)dxdy. Where S is surface enclosing region…

Q: Verify Green's theorem in plane for (x* - 2xy)dx + (x°y+ 3)dy where c is the boundary of the region…

A:

Q: 30 Find the volume of the solid generated by rotating the region bounded by the curve y= (x- 2)° and…

A: We first find the intersection of these two curve

Q: Evaluate the surface integral. xz dS S is the boundary of the region enclosed by the cylinder y2 +…

A: To evaluate the surface integral               ∬Sxz dS where S is the boundary of the region…

Q: ind the exact volume of the solid generated by revolving the region bounded by the given curves…

A:

Q: 5. Calculate the value of 7.îî dA over the whole surface of the cylinder bounded by x? + y? = 4, z =…

A:

Q: 2. Find the volume of the solid generated by rotating the region bounded by the curves y = Vx y = x…

A:

Q: 6. Evaluate ffſ z² dx dy dz taken over the volume bounded by the surfaces x2 + y² = a?, x² + y² = z…

A: Solution is given below:

Q: 2. Find the volume of the solid in the first octant bounded by the cylinder z = sin(y) when 0 < y <n…

A: To find the volume of the solid

Q: Let R be the region below bounded by the parabola y = 4 - x² and the lines 3x - 2y + 3 = 0 and y =…

A:

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x , y=0, x=TT/4, x= TT/2 ? ans/…

A:

Q: 1. Use a triple integral to find the volume of the solid that lies under the plane z = 1++y, and…

A:

Q: Subject:MMP

A:

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

A:

Q: Find the volume of the solid that lies under the surface z = 4 +y and above the region D in the…

A:

Q: Evaluate the surface integral. xz ds S is the boundary of the region enclosed by the cylinder y² +…

A:

Q: Express the double integral || (x+1)dA, where Q is the region in the upper half- plane (i.e. y20)…

A:

Q: Find the area of the surface given by f(x, y) = 8 + 4x – 5y that lies above the region R= {(x, y) :…

A: The surface f(x,y)=8+4x-5y that lies above the region R=x,y:x2+y2≤1.

Q: 1. Find the surface area of the cone z = √x² + y² that lies between the plane y = x and the cylinder…

A:

Q: Determine the area of the region between the two curves in the given figure by integrating over the…

A: We will find the area between the two curves as following

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: A) If the volume (1) of the region (D) enclosed by the surfaces (z = x² + 3y²), and (z = 8 – x? –…

A: Answer A:   The intersection between surfaces: x2+3y2 = 8 - x2 - y2 2x2+4y2 = 8 x2+ 2y2 = 4 (x/2)2…

Q: 3. Find the volume of the solid under the plane 3x+ 2y – z = 0 over the shaded region between the…

A:

Q: 4. Calculate the volume of the solid under the plane 4x + 2y – z = 0 and above the finite region R…

A:

Q: 2. Find the volume of the solid obtained whe the region bounded by the curve y = sin(x), 0 < x < ™,…

A: For the given information

Q: B. Find the volume of the solid generated when the plane region bounded by 3. y = e-x² and the x –…

A:

Q: raluate the surface integral. xz ds S is the boundary of the region enclosed by the cylinder y2 + z2…

A: S is the boundary of the region enclosed by the cylinder y^2+z^2=9 and the planes x=0 and x+y=8 S1:…

Q: Consider the region R delimited by the lines y=0, x=1 and the curve y=x^k. Let S be the solid…

A: The given region is: y=0   and   x=1  linesThe curve y=xk

Q: Set up a double integral that represents the area of the surface given by z = f(x, y) that lies…

A:

Q: Evaluate the integral. z dx dy da W is the region bounded by the planesx0, y 0,0, z-1, and the…

A: Evaluation of the triple integrals, uy conversion of cylindrical coordinates