Example 8: Find the volume of the solid whose base is bounded by y = x +1 and y = x², the cross sections prependicular to the x-axis are rectangles of height 5. 45 Ans. 2 -

Q: Suppose the following region is rotated around the y-axis to create a three dimensional solid. 4- 3-…

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Q: (1) Find the volume of the solid obtained by revolving about the y-axis the region bounded by y =…

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Q: The region between the curve y = 2/x and the x-axis from x = 1to x = 4 is revolved about the x-axis…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the x…

Q: The base of a solid is the region in the first quadrant bounded by the graph of y =1- and the z- and…

A: Since each cross-section is perpendicular to the x-axis is a square, we have to find the area in…

Q: Example 2 Determine the volume of the solid obtained by rotating the region bounded by y= Vx, x 8…

A: Region bounded by the y=x3, x=8 and x-axis

Q: Example 4: Find the volume of the solid generated by revolving the region bounded by y = x and y =…

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Q: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

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Q: 3. SET UP ONLY: Find the volume of the solid of revolution generated by revolving the shaded region…

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Q: 2. The area of the parabola x2 = 4y – 4 cut through its latus rectum is revolved about the…

A: 2) Parabola; x2=4y-4End points of the latus rectum (-2,2) and (2,2)vertem = (σ 1)using washer method

Q: 30. Find the volume obtained by rotating the region bound by the graph y = e²+e-2#, x = -2, x = 3…

A: Given that the region is bounded by y=ex+e-2x,  x=-2, x=3, y=0.And the region is rotated about…

Q: A region bounded by f(x) = 5 – x, y = 1, x = 1, and x = 3 is shown below. Find the volume of the…

A: The function of the curve is fx=5-x, y = 1, x = 1 and x= 3. The graph of the curve is shown above in…

Q: 6. Consider the infinite region in the first quadrant bounded by the y-axis, y = 1, and 1 y =…

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Q: 12. Find the volume of the solid that results when the region bound by x 1-y and the y-axis is…

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Q: 1. Sketch the graphs of v = 2x - x2 and y = - x. Shade the region bounded by the curves, Find the…

A: Given, The sketch graph of; Y = 2x - x² Y = - x The volume of the solid that is formed by revolving…

Q: 2.5 Find the volume of the solid of revolution formed by rotating the area under y = 9 – x? over [0,…

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Q: (10) Find volume of the solid whose base is the triangular region with vertices (0,0), (1,0), and…

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Q: The volume of the solid obtained by rotating the region bounded by y=4-x, y=0, X=-2, x-2 about the…

A: Determine for true or false

Q: 7) Suppose that y, =sinx and y, = cos x on [0,4] %3D Find the volume if the region between y, and y,…

A: First we sketch the region using a graphing calculator The shaded region is rotating about the x…

Q: A region bounded by f(x) = x, y = 1, and x = 4 is shown below. Find the volume of the solid formed…

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Q: 4. A solid is obtained by rotating about the x- axis. The curve is given to be as y = 3x² – x3 -…

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Q: What is the exact volume of a solid that is formed with a square base, aligned with the center of…

A: Now we will find the volume using the integration

Q: find the volume if it exists of the infinite solid of revolution formed when the area above the…

A: find the volume if it exists of the infinite solid of revolution formed when the area above the…

Q: 24 22. Find the volume generated by revolving about Ox the area bounded by the Ans. ra³. hyperbola…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: EXAMPLE 2 Find the volume of the solid obtained by rotating about the x-axis the region under the…

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Q: A region R is bounded by the curve y = ln x, the x-axis, and the vertical line x = e^2. If R is to…

A: Given curves are y=ln x, y=0 and x=e2 Region is revolving around x-axis. We have to find the volume…

Q: Consider the solid whose base is bounded by the x-axis and the curve y = f(x) = 9-x on the interval…

A: Here b=h

Q: 14. Find the volume tended by the graph of f(x, y) = 1+2x + 3y, the rectangle [1, 2] x [0, 1], and…

A: Given function is: fx,y=1+2x+3y and the coordinate of the rectangle is: 1,2×0,1

Q: 5. (6') Find the volume of the solid formed by revolving the area bounded by y = sin(x²), x E [0, T)…

A: Given - A bounded region To find - Volume of solid by revolving the region about specified line

Q: Suppose that a region R has area A and lies above the x-axis. When R is rotated about the x-axis, it…

A: Use the disc method to find the W in terms of V, k and A.

Q: 1. The region bounded by the curves y =7x and y=x² is rotated about the x-axis. USE THE METHOD OF…

A: Two given curves are  y=7x  (i)y=x2  (ii) The region bounded by these two curves is R and R is…

Q: 3. The base of a solid is a region bounded by the lines y = 2x−2 and y=−x+4 and the x- axis. If…

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Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2 A…

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Q: 4. A solid is obtained by rotating about the x-axis. The curve is given to be as y = 3x2 – x³. Find…

A: Let's find.

Q: A region bounded by f(x) = √√x + 2, y = 1, x = 1, and x = 4 is shown below. Find the volume of the…

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Q: 4. Find the volume of the solid generated by revolving about the line y=-3 the region bounded by the…

A: Using disc method, volume is evaluated.

Q: 5. Use Shells to find the volume of the solid generated by revolving the region in the first…

A: FORMULA FOR CYLINDERICAL SHELL METHOD V=2π∫ab(x-h)f(x)dx According to question, The volume is in…

Q: EXAMPLE 3 The region bounded by the curve y = Vx, the x-axis, and the line x = 4 is revolved about…

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Q: 1. The region bounded by the curves y = 5x and y=x² is rotated about the x-axis. USE THE METHOD OF…

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Q: 5. The area bounded by the graphs of y= 2x + 3 and y = x² revolves about the x-axis. Determine the…

A: Given y=2x+3 and y=x2

Q: (3+In x) Find the volume of the solid when the curve y=- is rotated 360° about the x-axis between x…

A: Using disk method volume is:  V=∫ee3πy2dx     =∫ee3π3+lnx3/2x1/22dx     =π∫ee33+lnx3xdx…

Q: EXAMPLE The region between the curve y = Vx, 0 sxs 4, and the x-axis is revolved about the x-axis to…

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Q: The region between the curve y = 1/x2 and the x-axis from x = 1/2 to x = 2 is revolved about the…

A: Graph the given situation, shaded region is being rotated about y axis

Q: 8. Find the volume of the solid obtained by revolving the region bounded by the graphs of y =-x cos…

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Q: Example 43: Find the volume bounded by the cylinder x + y = 4 and the planes y + z = 4 and z= 0.

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Q: 4. The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

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Q: Example 7: Find the volume of the solid whose base is bounded by the circle x2 + y² = 4, the cross…

A: Question 7: To find the volume of the solid whose area is bounded by the circle  x2+ y2 = 4, the…

Q: 5. Find the volume of the solid generated by revolving about the x-axis the region bounded by the…

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Q: 1) The region between the graph of f(x) = Vx In x and the x-axis, for 1 <x < e°, is revolved about…

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