EXample-Calculate the Volume of the object produced by the potar Curve e Zohe oseS/2 e turning around the axis o:/2wherer=+60s(8)

Q: 2. The length of a rod is 10 cm and the linear density of the rod at a point x centimeters from the…

A: Given that, the length of the rod is 10 cm, the linear density is ρ=2x+3gcm. Obtain the total mass.…

Q: An oil storage tank can be described as the volume generated by revolving the area bounded by y = x…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 80,0 < 0 <…

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Q: b) The area bound by the curve y = 2x + 1 and the y-axis is rotated about the y axis between y = 2…

A: We need to calculate the volume.

Q: Find the volume generated by revolving the area bounded by the curve y = (1-x²)² and the x-axis…

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Q: Find the volume gererot ed lby revolving the area bounded bay the parabolic arc Vx t vy = Ja and Hhe…

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Q: The linear density of a rod 3m long at a point x meters from one end is ke-3x kilograms per meter.…

A: Solution is given below:

Q: The area bounded by the curve y = x,y% = 2x and y = 4 is revolved about the line x =-2 Determine the…

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Q: Find the volume of the solid generated when the region bounded by the curve (x - 5)² = 4 - y and the…

A: Given:-the region bounded byx-52=4-y  and the x-axisrevolving about the line x=2using cylindrical…

Q: Example: Sketch the region enclosed by the given curves and find its area. y = V2x, y= =a², 0< x < 6

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Q: The closed curve x²+y²-14x-14y+49=0 revolves about the line x=-3. Determine the volume generated.

A: Given the closed curve is x2+y2-14x-14y+49=0 and the line x=-3

Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and ,x=-2 and x-5?…

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Q: Find the volume generated if the area bounded by the curve x2 = y - 2 is revolved about the x –…

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Q: Find the area of the surface formed by revolving the graph of y = 2√x on the interval [0, 9] about…

A: given that f(x)=2x . we need to find the area of the surface formed by revolving the graph y=2x on…

Q: Find the volume generated if the area bounded by the curve x² = y – 2 is revolved about the x-axis.

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Q: Find the center of mass of a thin plate covering the region between the x-axis and 20 the curve y =…

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Q: Find the volume generated if the area bounded by the curve y=x^2 and the line y=2x+3 is revolved…

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Q: Find the volume generated by the rotation of the region defined by the curve x=y2 and the line y=x-2…

A: Given: Curve x=y2 and the line y=x-2 and rotate the region defined by curves around the line y=-1.…

Q: Example 28 Find the volume of the solid obtained when the region bounded by the curve y= 3x, x- axis…

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Q: Use the linear approximation to estimate the percentage change in volume of a right circular cone of…

A: Let V,  r  &amp;  h be the volume, radius and height of the right circular cone respectively. Given,…

Q: A mineral deposit along a strip of length 6 cm has density s(x) = 0.01x(6 − x) g/cm for 0 ≤ x ≤ 6.…

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Q: 5. Find the volume of the solid generated by revolving the area bounded by the curve y = 4x - x2 and…

A: We are asked to find volume of the solid

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: Give an example of a plate such that its center of mass does not occur at any point on the plate.

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Q: Find the volume generated by revolving the area bounded by the curve y = (1 − x2)2 and the x-axis…

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Q: 1/ Find the area of the region enclosed between the curves y= 2x2+10 and y=4x+16 and ,x=-2 and x=5?…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Find the volume of the solid formed by revolving the curve defined by 9x²+4y²=36 about the line…

A: Given, The volume for solid revolution between the curves and around the on interval [0,1] The…

Q: find the volume of the solid generated when the region bounded by the curve (x-5)2=4-y and the…

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Q: The area bounded by the curve y^2 = 12x and the line x = 3 is revolved about the line x =3. What is…

A: Recall: Formula for volume,    V=π∫ab(radius)2dy Given,  y2=12x Substitute x=3 in the above…

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

A: Explained below

Q: Example 8: Find the volume of the solid whose base is bounded by y = x +1 and y = x², the cross…

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Q: The line x=-3 of the region bounded by the 2x=4-y2 and 2x=y2-4 curves Calculate the volume of the…

A: We first sketch the region using a graphing calculator. 2x=4-y2 (red) 2x=y2-4 (blue) x=-3 (green)

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 10, 0 < 0…

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Q: Use cylinder shell method to graph and find volume: y=sqrt(x), y=0, x=1, about x=-1

A: If a region is bounded by a curve y=fx and x-axis on the interval a,b and it is rotating about a…

Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and ,x=-2 and x=-5?…

A: Area under curve

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)=8x$ on the…

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Q: Find the volume generated when the area bounded by the curve y2=x , the line x=4 and the x-axis is…

A: Volume bounded by the curves, about y-axis.using Disk method

Q: Find the volume if the area bounded by the curve y = x³ + 1, the x-axis and the limits of x = 0 and…

A: (As per the guidelines, only 1st question will be answered).

Q: (a) Find that the area of the plane region lying to the right of the parabola x = and to the left of…

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Q: Find volume if area enclosed is rotated about y= -2.

A: To find the volume if the area enclosed by the below curves is rotated about y = -2.

Q: Find the area between the curves. 3x 3x x-0, x-D4, y3D2e" y-e

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Q: The area bound by the curve y^2 = 12x and the line x = 3 is revolved about the line x = 3. What is…

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Q: 3. [7 the graph of y = x3, on the interval [0, 1], is revolved about the Find the surface area of…

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Q: Find the volume generated by revolving about the line x - 4 = 0 the area bounded by the curve x2 =…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)= 9x5 on the…

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Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 8x³ on the…

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Q: 1/ Find the area of the region enclosed between the curves y= 2x+10 and y=4x+16 and,x=-2 and x-5?…

A: We use integral to find area bounded by curve and lines