75. Circular sector Integrate f(x, y) = V4 – x² over the smaller sector cut from the disk x² + y² < 4 by the rays 0 = 1/6 and 0 = T/2.

Q: Q3/ Find a center of mass of a thin plate of density 8 = 3 bounded by the lines x = 0, y = x, and…

A: Given region bounded by x=0 , y=x and parabola y=2-x2    in first quadrant

Q: 2) a) Ŝ find the value of the inter Specify the integrol liees |-x2

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Q: 5- 4- Find the volume of the solid created by rotating the following curve y = 3vx about the y-axis.…

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Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

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Q: 11. The solid whose base is the region bounded by the semicircle y = V1 - x² and the x-axis, and…

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Q: 8. The region in the first octant bounded by the coordinate planes, the plane y = 1 – x, and the…

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Q: What is the solid of revolution obtained when you revolve the region bounded by the curves y=x−1,…

A: We have given curves y=x-1,  y=0 and x=3 And we can plot graph of these curves as We can  see here…

Q: 5. Find the area of the surface obtained by rotating the curve about the x-axis: x' + 6. 1 <x<1 1 2x

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Q: A solid formed by revolving about the y-axis, the area bounded by the curve y=x4, the y-axis, and…

A: Given that  area bounded by the curve y=x4, the y-axis, and the line y=16.  To find the centroid of…

Q: 4) Consider a rod of length meters with density 8(x) =(2-cos x) kg/m over the interval 0sxS4. a)…

A: Solve the above questions.

Q: Find the area of the part of the eircle r-4 sin that lies within the sector 0 50s 87 -2/3 3 + V3 3.…

A: It is given that,r=4sinθ, that lies within the sector 0≤θ≤π3we have to find the area of the part of…

Q: The graph of y=x^3 between x=3 and x=8 is rotated about the x-axis. Find the surface area of the…

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Q: Use Green's theorem in order to compute the line integral £ (x – 3)³ dy – y³ dx where is the circle…

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Q: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

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Q: 2. Suppose you revolved the triangular region bound by the axes and the line 4x + 3y = 12 completely…

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Q: 4. Illustrate and find the center of mass and moment of inertia with respect to x and y for the…

A: y = f(x) =4-x2   only in First quadrant…

Q: 3 Find the abscissa of the centroid of the region between the parabola y = 9 − x2 and the line y…

A: Given :The parabola y=9-x2 and the line y=2-2x from x=0 to x=2.To find :The abscissa of the centroid…

Q: Find a center of mass of a thin plate of density 8 = 2 bounded by the lines y = x and x = 0 and the…

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Q: under the cone Z =Vx²+y² and above the region bounded by the semicircle X=-V 4-y and the y-axis.

A: The circle and a cone is given as,

Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x  about the line y=9…

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Q: Find the center of mass of a thin plate covering the region between the x-axis and the curve y =…

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Q: The triangular region Ω has vertices (1, 1), (2, 0), and (2, 3).

A: My=∫12∫-x+22x-1kx2dydx

Q: volume of solid of as revolution y^2=4x and x^2=4y about the x axis

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Q: 3. Find the length of the curve y = x – In x, 1<x < 4. 1. Find the area of the surface obtained by…

A: The solution is given as follows

Q: Show Z=arctan(y/x) satisfies Zxx+Zyy=0.

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Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

A:

Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: Work done= Force * distance                     =(force due to Weight)* distance

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Q: of fue Solid generekd by revolviny fel regine bounded by fue grapus of tue g pnd ful volume…

A: Apply the cylindrical shell method to find the volume of revolution, Consider a cylindrical shell of…

Q: 3. Find the surface area generated by rotating y=- bounded by y=0_ x=0 , and x=9 about the the…

A: Surface area generated by rotating a curve y = f(x) about the x-axis from x = a to x = b is given by…

Q: 8. cos x sin y dx +(3xy+sin x cos y) dy and y = \x 4oil C:boundary of the region lying between the…

A: Given that ∫Ccos x sin y dx+(3xy+ sin x cos y)dy ;y=x4, y=x Using Green's theorem ∫CP dx+Q…

Q: Find Ihé volume of Ihe solid whose base is Ihe region bounded by y=x² and y=1-x², and whose cross-…

A: Given that y=x2,y=1-x2 The formula to find the volume is, V=π∫abf(x)2-g(x)2dx To find the a and b,…

Q: 2/ Find the line integrals of the ellipse+3= ellipse by x = acos(t) ,y= bsin(t) 1 , parameterize the…

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Q: find the center of mass of a thin plate of constant density d covering the given region. 1. The…

A: Given information:

Q: 1/6 Find the volume of the solid obtained by rotating the region bounded by and リー2) about the line…

A: Now , we will find the  volume of the solid  obtained by rotating the region bounded by the given…

Q: Calculate the volume of the solid generated by the rotation of the region formed by y = arc cos (x),…

A:

Q: Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the…

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Q: 2. The solid bounded by y = 0, x = y², x = 4, and z = Octant (ie. x, Y, z > 0). 2x in the First

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Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

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Q: :-1, 8. Find the volume of the solid obtained by rotating the region bounded by the curves y = y =…

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Q: Find the solid of revolution that results when the region under the graph of f(x) = xvsin x for 0< x…

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Q: The triangular region with corners (6,0), (7,0) and (7,3) is rotated about the line x = –1. The…

A: Given - Vertices of triangle and volume of solid  To Find - Constant in the expression of volume

Q: The area under the curve 4y2 =" (x2 + 1)3 was rotated about a line located to the left of y – axis…

A: The surface area of the solid can be obtained using the Pappus theorem. The surface area is…

Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: set up the integral for w9rk requireded to pump the water in the drum shaped solid to the goal line

Q: 2. Find the volume OF solid obtained by revoluing region bounded the about x- axis x2 and the the by…

A: Given that, the curve is y=x2 and the lines are x=0 and x=2. Note that, the formula for the volume…

Q: Find the abscissa of the centroid of the region between the parabola y = 9 − x^2 and the line y = 1…

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Q: 4. A right and uniform solid cone C of mass M has a height 3R and a circular base of radius R. By…

A: The equation of Centre of mass C =\frac{\int \rho hdV}{\int \rho dV}C=∫ρhdV∫ρdV Where ρ is the…

Q: 2. Find the volune og the solid gonned by revohing abaut thie lere y y=4x+1, y: -1 bounded by 4x +3,…

A: The volume for solid of revolution generated by revolving the area bounded by curves y=f(x) and…