Find the arua g falloming pai 1 unus. , メ=y-y,y=> the rigion bounded by the 1, メニリーダ メ=y x = 4y-y° ウ× find Hint: gut fist the pninto f the perabola and line Vse hangontal ilement to fend the area intersection

Q: 3. Find the volume of the object cut from the cone z = Vx² + y² by the plane z = 1.

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

Q: "ind the centroid of the quarter circle x + y <7, y 2 |x| assuming the density ő(x, y) = 1. Use…

A: We need to find mass(M) and moment of inertia about x and y axis of the lamina  Mass of lamina…

Q: Find the area of the surface of revolution r(u, v)= 6sin(u)cos(v)i+ 6uj+6sin(u)sin(v)k, where 0SusT…

A:

Q: Evaluate ze dV, where E is the portion of the ball centered at the origin of radius 5, x + y+< 25…

A: Given Where E is portion of the ball centered at origin, radius 5 and lies in first octant. In…

Q: Find the surface area of the portion S of the cone z^2=x^2+y^2 where z≥0z≥0, contained within the…

A:

Q: Consider the parallelepiped with adjacent edges u = 5i + 2j + k v=i+j+ 7k w = i + 9j + 5k Find the…

A: Given, u=5i+2j+k,v=i+j+7k,w=i+9j+5k.

Q: Use cylindrical coordinates (15.7) to find the volume (8) Q is bounded by the paraboloid z = 9– x² –…

A:

Q: Find the volume of the solid bounded by the paraboloid z= 20 - 5x? - 5y and the plane z = 15 V =…

A:

Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

A:

Q: integrate ƒ over the given region. ƒ(u, y) = y - sqrt(u) over the triangular region cut from the…

A:

Q: Türkçe: z = 16 - x? – y? paraboloidi, x? + y? = 8 silindiri ve xy-düzlemi ile sınırlandırılmış katı…

A: Given, z=16-x2-y2 paraboloidx2+y2=8 circle To find: Volume of solid

Q: 6l@) n spnenical oordinates (p,O,Ø), the equation Ô = C where C s a constert repretents in eg. á…

A: (a) In spherical coordinates, ρ,θ,φ, θ is the angle made by the position vector with the z-axis,…

Q: Consider the parallelepiped with adjacent edges u = 3i + 3j + k v = i+j+ 8k w = i+ 8j + 4k Find the…

A:

Q: Q5) Find volume of body bounded by z? + y? + x? = 9.

A: Let's find.

Q: Consider a unit disc of radius 1 centred at the origin. The straight lines y = x and y =-x break…

A: Plotting the y=x   ,   y=-x and  unit circle center at origin on the graph and dividing into TOP,…

Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

A:

Q: find volume 26. The wedge cut from the cylinder x2 + y? = 1 by the planes z = -y and z = 0

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: Calculate /| xz dS, where K is the part of the cone z = Va2 + y? where z < 2.

A: Given the surface

Q: Use cylindrical coordinates to calculate fSfw f(x, y, z) dV for the given function and region: f(x,…

A:

Q: nd the surface area of the part of the plane z + 4y + z = 2 that lies inside the cylinder r +y° = 9…

A:

Q: 8. Evaluate ze+y´+z² dV, where E is the portion of the ball centered at E the origin of radius 5, x?…

A:

Q: 2yx dA ; R={(x,y):0sxs1,-1<ys2} y+3

A:

Q: Find the orthogonal trojectories of y(sx +c) = 1.

A: Given query is to find the orthogonal trajectories to y (3x+c) = 1.

Q: 4) çalculate [ 4XdA on disk R which is the region bounded by Y = X² y la recta X – Y + 2 = 0. A) 7…

A:

Q: Consider the parallelepiped with adjacent edges u = 7i + 3j + k v = i+j+ 7k w = i+ 5j + 7k Find the…

A:

Q: Find the area of the lateral surface of G z=x^2+3y^2 and below by the plane z = 0, and laterally by…

A:

Q: find the volume of the region de limited by S the sm face parametu zed by R(u, u) - sin (u) cos(v)i+…

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: 8 Use the shell me fthe t to find the vo lume of the solid the plane' rejion akout the Line ited by…

A: Given: Find volume about line x=6 The region between the curves y=x y=0  x=4 Volume using shell…

Q: Find the points on the cone z = x + y2 that are closest to the point (8, 2, 0). %3D (x, y, z) =…

A:

Q: WY = WZ bail M is the midpoint 40. Given: of YZ MX 1 WY MT 1 Zojpib tisz ow Prove: MX = MT 41.)…

A:

Q: Let S be a square plate with boundary C having length of each side as 2 units, lying in the plane z…

A:

Q: Use cylindrical coordinates to calculate SS lw f(x, y, z) dV for the given function and region: f(x,…

A:

Q: Calculate the area of the surface S. x2 y² _ z2 that lies between z = 2 and z = 6. S is the portion…

A: Explained below

Q: Consider the parallelepiped with adjacent edges u = 3i + 2j +k v = i+j+4k w =i+6j + 2k Find the…

A:

Q: B is the first quadrant part of the region enclosed by the circles x2 + y? = a? and x2 + y? = b2…

A:

Q: Let B be the ball with center at the origin and radius 1 SIS 4(z² + y² + z*)dv = B

A:

Q: Evaluate /VT² + y² dV_where E is the region that lies inside the cylinder E x² + y? = 4 and between…

A:

Q: Consider the parallelepiped with adjacent edges u = 5i + 5j + k v = i+j+ 8k w = i+ 5j + 7k Find the…

A:

Q: Find the equetion of the targent pane to tre grven Surfface at the Specified point Z=XSin(x+y) at…

A:

Q: For the conical surface 0 = 30°,0 <0< 21,0 <r< 2, the lateral surface area is what?

A: Sol

Q: Consider the parallelepiped with adjacent edges u = 5i + 7j + k v = i+j+2k w = i+ 9j + 2k Find the…

A:

Q: Q5) Find volume of body bounded by z? + y2 + x2 9.

A: Given that - x²+y²+z²=9 =&gt; (x-0)²+(y-0)²+(z-0)²=3² Clearly which is a sphere with radius,r= 3…

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

A:

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

A:

Q: Con vert to cylin drical and e valvate: dV Where Dis The region between the planes z=1 aud z =4 and…

A: Given integral is, ∫∫∫D2ex2+y2dV Where D is the region between the planes z=1 and z=4 and inside the…

Q: Find the area of the part of the cone S = {(x, y, 2); z = Vx² + y?, x²+y² < 1}.

A: Given surface is S=x,y,z:z=x2+y2,x2+y2≤1 We have to find the area of the surface. Here, z=x2+y2…

Q: Find the volume of the first-octant portion of the "wedge" of the sphere x? + y? + z? = 64 bounded…

A: