13. Region bounded by: y = 4 – x and y = 0. - Rotate about: (а) the x-axis (c) y = -1 (b) у — 4 (d) x = 2

Q: 8. The region of integration D is bounded by the lines y = x,x + y ==,y = 0. Show that 1 | sin(x +…

A:

Q: 11. , e-y dA, where D is the region bounded by the semi- circle x = V4 y2 and the y-axis licated, in…

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Q: Determine a region of the xy-plane for which the DE (y- x) y' = y+ xwill have a unique solution…

A: Consider a differential equation y'=F(x,y), y(x0)=y0. Then there exist a unique solution to this…

Q: 28 The region in the first quadrant bounded by y rotate about the line x = 4x2 , 3x + y = 7, and the…

A: It is given that, the first quadrant bounded by y=4x2,3x+y=7 and the y-axis is rotate about x=-4.…

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

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: 3 - Find the bounded ly y=2x-2, x=-1, x= 2 3 area y=2X - 2, x=-I, x= 2 4- Find the anea bondol .

A: Integrate the given parabola from x=-1 to x=2

Q: 1 10. Rotate the region bounded by y=y=9, x = -2, x = 3 about the x-axis.

A: Note: Volume V of revolution about the x-axis is given by V=∫abπ y2dx .

Q: 2. Region bounded by y= x, x=0 and y=15, rotated about the y-axis

A:

Q: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: Q. No. 4 Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y =…

A: Given lines are, y=x and y=2-x

Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

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Q: Volumes of solids Find the volume of the following solids.

A: The region is bounded by the curves, The region is shown in the graph given below,

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

Q: 17. Region bounded by y = 2x, y = x and x = 2. Rotate about: (a) the y-axis (b) x = 2 (c) the…

A: As per company guidelines we are allowed to solve maximum three sub parts so i am solving first…

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

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Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: 3. Find the olume of the solid generated by revolving about the line z--4 the region bounded by that…

A: Here is the solution of the given problem

Q: - The region bounded by y = 2 -x, y = 0, x = 1, x = 2 is rotated about the x axis. 197/12

A: volume generated by revolution of the solid is 19π12 detailed solution with explanation is given…

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

A: Given  The function is ƒ(u, y) = y - √u . The triangular region cut from the first quadrant of the…

Q: y=x², y = 1, y =9 y=9, first quadrant

A:

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

A:

Q: 2. The region bounded by x = 2 y, x = 0, y = 9 is rotated about the y - axis.

A: Given Data: The given curve is x=2y. Rotated about y axis. The limit for y axis is (0, 9).

Q: 3. Region bounded by Y = rotated about the x-axis ,x=0 and y=15,

A: By shell method

Q: 4. Region bounded by y = x2, x=0 and y=15, rotated about the y-axis

A: Imagine the plot and rotate it about the axis specified and the resulting figure will lead to the…

Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: Compute where Cis the counter clockwise oriented boundary of upper-half unit disc D. 0.66666666667…

A: We need to find ,  ∮ y2dx + 3xydy , over  C ,  where C is the counter clockwise oriented boundary of…

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

A: My=∫12∫-x+22x-1kx2dydx

Q: 12 - Which of the following is the volume of the object that occurs when the region bound by the…

A: We sketch the region using a graphing calculator  The shaded region is rotating about the y axis

Q: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

Q: 4) Find the centroid of the region that is bounded by the X axis, the Y axis and the line that…

A:

Q: 13. Region bounded by: y = 4 – x and y = 0. Rotate about: (a) the x-axis (c) y = -1 (b) у 3 4 (d) x…

A: We are authorized to solve only one question with 3 subparts, please repost remaining questions…

Q: 3. The region bounded by y = x³, y = x, x > 0 is rotated about the x – - axis.

A:

Q: 3. Evaluate ff Vr² + y²dA, where R is the region bounded by the circles with center R (0,0) and…

A: Given integral is: ∫∫Rx2+y2dA Where R is the region bounded by the circles with center 0,0 and…

Q: 2. Find the center of mass for the region bounded by y = 4 - x2 that is in the first quadrant

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Q: Use Polar coordinate to evalute ff gdA, 8 where R is the region Bounded by the life line yet, the…

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Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

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: 6 Find the center of mass of a thin plate of constant density & covering the region in the first and…

A: Calculate center of mass for x coordinate: x=∫x=01∫y=-61+x261+x2xdydx∫x=01∫y=-61+x261+x2dydx…

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: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

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Q: 20- What is the share of the formula that allows calculating the y coordinate of the center of…

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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: 1. Region bounded by y= x, x=0 and y=15, rotated about the x-axis

A: Volume of solid revolve around y axis

Q: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y-y3, x…

A: Consider the graph:

Q: Solve the Boundary Value Problem yet(x, t)=9yxx(x, t), 00 y(0,1)= y, (3, t) = 0, >0 ye(x,0) = 0,…

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