Question 49 Use multiple integrals to find the volume of the indicated solid. 8- z-8-2y 6- 4- y. 3. 0Sys3 O 24 O 32 O 48 O 60 Next 9:05 AM A ^ ENG 20/09/2021 2.

Q: a single integral whose value is the area of the region bounded by the curves y = 12−x^2 and y = x^2…

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Q: y = V(4x – x²) (1+0.25x + 0.25 sin(x))

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Q: The region is bounded by x+6=0 and y^2+x+2=0 is revolved about x=-6. find the integral in finding…

A: Consider the provided question, The volume for solid of revolution between the curves x+6=0 and…

Q: sketch the described regions of integration.0 ≤ y ≤ 1, 0 ≤ x ≤ sin-1 y

A: Given: 0≤y≤1 0≤x≤sin-1y

Q: dydx tan x 1. 1+ y?

A: We will solve the following

Q: 8. Sketch the region bounded by the graphs of the equations and use iterated integrals to find its…

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Q: Each integral represents the volume of a solid.Describe the solid.   ∫0π/42 π (π - x) (Cos x - Sinx)…

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Q: With the help of simple fraction s separation method dx Caleulate the integral.

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Q: Is there a dxdy integral that would need to be broken up into two integrals if switched to dydx…

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Q: 1-r x² + y² dydx

A: Area of a function fx, y for a≤y≤b is given by  ∫abfx, ydy So, ∫-1-x21-x2x2+y2dy represents the area…

Q: 5.0⁰0 x² - 2x+6 (x²+2)(x-2) -dx

A: We have given a Improper integral ,  I = ∫3∞ x2 - 2x + 6x2 + 2x -  2dx We know that , Improper…

Q: How to compute for the differential volume of each coordinate system and its phase area?

A: Hints: We have to discuss that how to compute for the differential volume of each coordinate system…

Q: If we want to find the area between the curves x = −y 2 + 1 and x = y 2 − 1, shall we integrate with…

A: Given curves are x=-y2+1 and x=y2-1

Q: The curves x = 4y - y^2 and x = 2y - 3. Set up a single integral that evaluates the shaded area and…

A: Given  x=4y-y2 ,x=2y-3  To find  Area between  given curve using single integration method

Q: 3 4 Sx-3 dx x2+8x+41 (x+2)2 x2+9

A: Given,          ∫2x-3+3x+22+4x2+9+5x2+8x+41dx

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. ∫ x2e2x dx

A: Known fact: ∫u dv=uv-∫vdu

Q: the region bouded by x=y+2 and x=y^2 revolved about x=-1. Find the integral in finding the volume of…

A: The volume of the solid generated by revolving about the y−axis a region between the curves x = f(y)…

Q: Set up an integral to represent the total mass of a 2×5 rectangular sheet, whose density per unit…

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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: y y=x + 1 x = 4 y= 0

A: Area , A = ∫∫R dy dx

Q: By using integration by parts, the value of the integral In 2x dx

A: The given integration is ∫ln 2x dx

Q: Sketch the region of integration for the double integral given by integral 0 to ln2,e^x to 2 dydx…

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Q: Set up the the integral to find surface area for f(x)=x^4+1 over [1,3] show all steps for setting up…

A: The solution is given below

Q: 25 dr. valuate the integral: re

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Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. ∫ ln 5x dx

A: Given that, ∫ ln 5x dx We have to find u and dv to use by parts.

Q: 4 L, cos-"(2x) Voz int(acos(2*x)*sqrt(exp(pi/2),4,-6) int(acos(2x)*sqrt(exp(pi/2),-6,4)…

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Q: Find the exact value of he integral using a formula from geometry or any other method. ∫ ( 6 upper…

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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: 2. Find the volume of a cylinder with a radius of r and height h by integration.

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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: Sketch the graph. Set up (DO Not Evaluate) an integral for the volume of the solid that results when…

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Q: How to find Volume and Surface area of above problems using integration?

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 5. The area bounded by the curve y = 3x – x3 and the line y = 2 is revolved about the line y = 2.…

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Q: x² 5. y = 4 In x 1<x<4

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Q: 9. The area bounded by the parabola x 4y and the line x = 4 - 2y is revolved about the line y 4.…

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Q: How do you find the upper and lower limit of an integral volume equation?

A: To find :  The upper and lower limit of an integral to find the Volume of the given region.

Q: Each integral represents the volume of a solid.Describe the solid.   ∫032 π x5 dx

A: Given : ∫03 2π x5 dx=?…

Q: 2. The area bound by the curve y = ezr, the y – axis and the line y = 4 is rotated about the line y…

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Q: Sketch the region whose area is given by the definite integral. 25 y 2 0.5 2.5 yA.5 y 2 2x

A: Let fx=2-x=2+x        -2≤x≤02-x          0≤x≤2 Now for -2≤x≤0 Graph of fx=2+x is a line segment with…

Q: Consider the region bounded by the graphs of y 2e 1, y = e", and y = 2 shown in FIGURE 6.2.12.…

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Q: 1) z = 2 – x² – 2y², z = 1

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Q: Evalute the fellowing g internel,

A: Formulae used: ∫xndx=xn+1n+1+C∫1dx=x+C∫sindx=-cosx+C∫cosdx=sinx+C

Q: Evaluate the double integral that will solve for the area of the region bounded 2. by y = cos (x) +…

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Q: Find an approximation of the area y = 16 - x² over the interval [0,4] using L6 (left end point…

A: Use: Area=∆xf(x1)+f(x2)+f(x3)+f(x4)+f(x5)+f(x6)       where ∆x=b-anwhere n= no. of rectangle…

Q: 3. Use differentials to approximate the volume of a spherical shell whose inner radius is 5 cm and…

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Q: (2,2,0)

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Q: A solid is generated by revolving about the x-axis the region in the first quadrant bounded by the…

A: It is given that, y=1+sin2x,x=π2   Volume of solid formed by revolving the first quadrant region…

Q: . The area bounded by the curve y = 3 – 2x + x² and the line y = 3 is revolved about the line x = 5.…

A: The volume of the solid of the revolution can be calculated using the shell method. The formula to…

Q: 10. f3, (x²-1) dx

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Q: Use a double integral to find the volume of the indicated nolid. 12 z- 12-X-y 11 10 4. 6. y 6 y-x

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