The second question: very result 1- La xcos(y²)dydx 2- S S, Vx² + y²dA located in the first quarter x - 2x + y = 0 where ( is the area defined by the curve

Q: Q. 3 The solid of revolution obtained by rotating the region under the curve y = f(x), a sx sb,…

A: Formula: uv'=uv'+vu' Formula: sin x'= cos x The given function is: f(x)=x sin x, 1≤x≤2 The surface…

Q: a) Evaluate x In (2.x) dx by using integration by parts b) Find the area bounded by the curve x- 3+…

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Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the…

A: Given: y=3x3 for 0≤x≤1

Q: 8. y = f(x) impending 8y?=x?- xu, 1 4. calculate formed as definite integrål. the surface area…

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Q: The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area…

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Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e 3x. (Use…

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Q: Q3/A/Find the surface area generated by rotating the curve y = cos h(x) about x axis for 0≤x≤1

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Sketch the region whose area is represented by the definite integral. dx y 12 12 10- 10 8. 6 6 10 2…

A: The definite integral can be used to evaluate area of region bounded by curves. If over an interval…

Q: Set up the definite integral for the area of the surface of revolution about the x-axis. Do not…

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Q: (b) Use Simpson's Rule with n = 10 to estimate the area of the surface obtained by ro the cosine…

A: I have solved b part as asked.

Q: 16 The area under the curve 4y? (x2 + 1)3 was rotated about a line located to the left 9 of y – axis…

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Q: 15. a) Sketch the region enclosed by the linex = 3 and y = 1 and the curve xy = 9, %3D and find its…

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Q: 16. Compute the surface area of the surface obtained by revolving the given curve about the…

A: To compute the surface area of the surface obtained by revolving the given curve about the axis x =…

Q: If the curve y = ln x between x = 1 and x = e is rotated about the y-axis, which integral below…

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Q: 3. Let R be the region below bounded by the parabola y = 4 – x2 and the lines 3x – 2y + 3 = 0 and y…

A: The given curves are y=4-x2, line: 3x-2y+3=0 and y=0. To find: (a) definite integral such that it…

Q: Sketch the region bounded by the curves y=e* , y=0, x=-1 and x=1. ...

A: The region bounded by the curves is shown in the figure below

Q: 1) The Arc Length of the curve f(x) = coshx, 0≤x≤ In3 is: d. 1/1/22 4 12 a. b. ³/1 3 2) The Volume…

A: Given

Q: Find the area enclosed by the curve x = t2 - 4t, y = -Vt and the y-axis. A = S rdy or A= S. (TR-IL)…

A: x=t2-4t, y=-ty=0 →t=0y=-2 →t=40≤t≤4dydt=-12t

Q: Question 8. Use a change of variable to compute the integral 10 R x+ y where R is the triangular…

A: To evaluate the integral by changing the variables x,y into the new variables u,v, use the following…

Q: The surface area of the surface generated by revolving y=1-x² for 0<x<1 about the x- axis is s=…

A: If you like the solution then please give it a thumbs up.... The Answer is:              S =…

Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

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Q: Evaluate the line integral ſ. 8y² dx + z² dy + (100 – x²) dz over the quarter of the circle of…

A: To evaluate the below line integral. ∫c8y2dx+z2dy+100−x2dz Here c is the quarter of a circle of…

Q: Q2: Find the surface area generated by rotating for y = x² - ln(x) for x = [1, 2] about the y-axis.

A: We need to find Surface area.

Q: b. The triple integral in Cartesian coordinates JIT »z dv that gives the value of FIRST octant…

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Q: Set up the integral for the Surface Area of the curve y = In(x) from (1, 0) to (e, 1) %3D rotated…

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Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

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Q: 3. By using Green's Theorem in the plane, evaluate | (y - sinx) dx + cos x dy where C is the…

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Q: 2.) Find the exact area of the surface obtained by rotating the curve about the x-axis y= cos(÷x) 0…

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Q: 1 y = f(x) impending 8y² = x² – x*, V3 1 To Find: Surface area of the rotating body formed by…

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Q: The surface area of the solid of revolution generated by rotating x = (y² + 2)²,1 < y s 2 about the…

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Q: 4. Set-up and evaluate the definite integral that represents the area of the surface generated by…

A: Formula: The area of surface generated by revolving x=f(y), a≤y≤b about x-axis is given by,…

Q: Let S be the surface area generated by revolving the curve y = Vx, 2 < x < 12 about the x- axis.…

A: This formula is used

Q: 2. Given: region R below bounded by the graphs of y = VI – 1, y = 3- x, and y = 0 (2, 1) R (1,0) (3,…

A: The arc length of the curve y=f(x) over a≤x≤b is given by: L=∫ab1+(f'(x))2dx...(1)

Q: Set up an integral for the area of the surface generated by revolving the curve y = x2 about the…

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Q: 19-22 Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the…

A: Given:    y = x + x2     0 ≤ x ≤ 1

Q: E valuate the area bounded by the parabola the Parabola X= y omd integral X = 2y-y using double

A: Please see the graph below to first understand what's going on:

Q: 8) Find the area of the surface generated by rotating about the x-axis the arc of the curve y x…

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Q: 10. Use a definite integral to find the exact area enclosed by the x-axis and the parametric curve =…

A: The given parametric curve is: x=2t3+1    and     y=2t-t2

Q: The area of the surface generated by rotating the curve y = 2 + e*, where 1 < x < 2, about the…

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Q: Express the area of the surface obtained by rotating the curve y =In sec(2x) between x = 0 and x =…

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Q: 1r + 3x + 18, The region R in the first quadrant of the xy-plane is bounded by the curves y = x = 0…

A: Given: The given curve is y=-x2+3x+18,x=0 and y=0.A solid S is formed by rotating R about the…

Q: 1 (#3) Find the surface area for y = 3 on [0, 3] rotating on the x- axis.

A: Given an equation of a curve, The solid will form by rotating the curve about the x-axis.

Q: Consider the region which lies between the line y = x-1 and the semi-parabola y =; Express the area…

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Q: 5. The external fuel tank for a space shuttle has a shape that may be obtained by revolving the…

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Find the area of the surface generated by revolving the curve x = 4 1 from 8y 3 < y< 5 about the…

A: When a function is of the form x=g(y) and you are revolving around the x-axis, the interval is c≤y≤d…

Q: ху — 4, 1 <x< 8

A: Surface area.

Q: 2. Find the volume of the solid obtained whe the region bounded by the curve y = sin(x), 0 < x < ™,…

A: For the given information

Q: Given x= In(2y+1), 0<y<l. a) Set up an integral for the area of the surface obtained byrotating the…

A: The curve given is as follows: fy=x=ln2y+1,  0≤y≤1 (a) Differentiate the function.…