1) The region is defined by y= e", y = 0, x 0, x=1. Rotate the region about the: a) x-axis b) y-axis c) the line x =1 d) the line y = e

Q: Given that p, = x² +xy, calcultae p, ds, over the region, y <x,0 <x < 1.

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Q: 4. Find the volume of the region bounded above by the paraboloid z = x? + y? and below by the…

A: (4) Consider the provided question, According to the provided question, draw the graph of the given…

Q: Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

A: To evaluate :   ∫C6xy6ds, where C is the right half of the circle x2+y2=4 Prerequisite : We can…

Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

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Q: Evaluate , ydV where E is the hemispherical solid region x? + y? + z? 0.

A: x^2+y^2+z^2 &lt;=64, y&gt;=0

Q: (2) Sketch the following region R. R= {(r,0) : 1<r < 3, 1/2 <0< 2n}

A: Sketch the following region R

Q: 3. Find the volume of the tetrahedron in the first octant that is bounded by the three coordinate…

A: Given the equation of the plane, z=5-2x-y  ⋯⋯(1) Rewriting equation (1), 2x+y+z=5  ⋯⋯(2) At z=0,…

Q: A solid is constructed so that one side is the region between the lines z = a, x = b, the graph of y…

A: The cross-section of the solid are perpendicular to the x-axis and are isosceles right triangles so…

Q: Sketch the region enclosed by the given curves. y = 3 cos(5x), y= 3 – 3 cos(5x), 0 < x< 1/5 y y 6- 2…

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Q: find the ora of the Region described t vegion bounded by gee"iy=e EIny and

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Q: Suppose a sphere of radius r is sliced by two horizontal planes h units apart (as shown). Show that…

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Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

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Q: a) Evaluate [(2x- y' )dA over triangular region R enclosed between the lines y = -x +1, y = x+1 and…

A: Given integral is ∫∫R2x-y2dA, where R is the triangular region R enclosed between the lines y=-x+1,…

Q: Consider the parallelepiped with adjacent edges u = 5i + 2j + k v = i+j+ 7k w = i + 8j + 2k %| Find…

A: The volume of the parallelepiped is 253

Q: A solid is constructed between the graphs of y = f(x) and y = g(x) and the lines æ = a and æ = b so…

A: Given figure,

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

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Q: Integrate the fallswingfuntinne aver the given regionr s R: the circle x+y=t and y=x? thiss

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Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

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Q: Show the triangular region bounded by the lines x = 0, y = 0 and x + y = 1 is invariant for the…

A: Given: It is given that, the triangular region is x=0, y=0 and x+y=1. To prove: We have to prove…

Q: Let R be the region bounded by y the solids obtained by revolving Rabout each of the following : (a)…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: 5. Use the method of Washers and Shells to find the volume of the solid generated when the region R…

A: Given, y=x2over [0,2] is revolved about the line y=-2.

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: 17. Use the method of disks/rings to determine the volume of the solid obtained by rotating the reg…

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Q: 1- Find the volume of the solid generated be revolving the shaded region about the given axis. About…

A: The volume of the solid generated when the first given region is revolved around the y-axis is to be…

Q: Let CR be the circle of radius R centered at the origin. Use Green's Theorem to find the value of R…

A: ∮ y3 dx+x dyUsing green's   theorem∮P dx+Q dy=∫R∫∂Q∂x-∂P∂y  dAP=y3                  Q=x∂P∂y=3y2…

Q: Sketch the region enclosed by the given curves. x = 9y2, x = 28 + 2y2 y y 21 35 30 1 25 20 5 10 15…

A: x=9y2,  x=28+2y2 The region is,

Q: Consider the parallelepiped with adjacent edges Find the volume. u = 2i + 7j + k v=i+j+7k w = i +4j…

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Q: 1. SSR ry? dA, where R is the region in quadrants 1 and 2 bounded by the semicircle of radius 2…

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Q: 1. SSR ry? dA, where R is the region in quadrants 1 and 2 bounded by the semicircle of radius 2…

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Q: 7. Find the volume and centroid generated by revolving the given plane area about y^2=4x, x=4; about…

A: Given that - y2 = 4x, x = 4; about x = 4

Q: Draw the solid of revolution obtained by rotating the given plane region about line L. Which figure…

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Q: Determine a region of the xy-plane for which the given differentail equation would have a unique…

A: Given differential equation (y-x) y'=y+x   or    (x+y)dx+(x-y)dy=0 Note that differential equation…

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: 2. Sketch the two dimensional planar region R = {(x, y) | 0 <x < 2, x² < y < 2x}.

A: Solution Given Seetch the two dimensional planar region R={(x,y)|0≤x≤2,x2≤y2x}

Q: ind the volume of the solid generated by revolving the region bounded by the graphs of the equations…

A: please refer to the image below.

Q: Let W be the region that is cut aut from x't v<4 by the pora blae id Rs X'ty ond the plane =10.…

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Q: (1) Compute where Cis the couater dockwise oriented boundary of upper half unit disc D.

A: It is given that, ∮Cy2dx+3xydy here C is counter clockwise oriented upper half disc D.   Here,…

Q: If the region bounder by the two curves is revolved about x = 4, what is the volume of the resulting…

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

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Q: As discussed by our text in 16.6, the centroid of a 2D region is at cartesian coordinates (7, 9),…

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Q: . SS, xcos(y)dA, D is bounded by y = 0,y = x² ,x = 1.

A: See the details solution in below

Q: (b) Prove the volume of a parallelepiped with a vertex at the origin and edges ü,v, and w is given…

A: In the question we have to prove the formula.

Q: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).

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Q: Sketch the regions enclosed by the given curves. y = Vx, y = Ex, x = 9 y y 5 5 4 3 3 1 1 X 2 4 6 8…

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

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Q: Use the method of disks to rotate a circle of radius r around the x axis and prove that a sphere of…

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Q: find volume 31. The region in the first octant bounded by the coordinate planes, the plane x + y =…

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Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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Q: The volume of the tetrahedron bounded by the plane * ++ = :1, {a, b, c > 0} and the coordinate a…

A: Volume of the figure will be given by integral - V = ∫∫∫dzdydxLet's find limits of z,y and x - Given…