О 3D 2х — у, 1

Q: Set up the integral to find the surface area of the volume generated by the curve y=1/2 (x −3)^2…

A: Given, a=0,b=2  y=1/2 (x −3)^2 +1/2 Therefore, (2y-1)/2 = 1/2 (x −3)^2 2y-1= (x-3)² Taking square…

Q: Let S be the shape obtained by rotating f(x) = 2 /x +1 on the interval [1, 3] around the x-axis.…

A: Given :fx = 2x+1

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

A: Explained below

Q: Find the surface area of revolution about the x-axis of y=3sin(5x)y=3sin(5x) over the interval…

A: I am attaching image so that you understand each and every step.

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

A: Please refer the attached image for complete solution.

Q: Let R be the shaded region bounded by the parabola y = 4 - x², and the lines y = 1- 2x and y= -1, as…

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Q: compute the surface area of revolution about the x-axis over the interval. y= x3, [0, 2]

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Q: Set up and evaluate the definite integral for the area of the surface x2 y = 1 - 16 OsxS 4 2n dx =

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Q: The surface formed by rotating the curve y = x 2 1, about the x-axis is known as Gabriel's horn.…

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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…

A: Recall: Area of the Resulting surface rotated about x-axis : If the curve y= f(x) ,a≤x≤b is rotated…

Q: Then, compute the surface area of the solid that is formed by rotating y = In(x) on [0, n] about the…

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Q: Find an integral to represent the area of the surface obtained by rotating the curve x= (y - 2)3/2…

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Q: Find an integral for the area of the surface obtained by rotating y = √25-x, 9 ≤x≤ 16, about the…

A: To find an integral for the area of the surface obtained by rotating the below equation about the…

Q: Which of the following integrals will find the area of the surface generated by revolving the curve…

A: fx=x3 is a polynomial function. It is continuous in the interval 0,3.

Q: Sketch the region R bounded below by the curve y = x², on the left by the line x = 1 and above by…

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Q: Use an appropriate change of variable to evaluate the double integral: cos dA, R where Ris in the…

A: Given integral is  ∫∫Rcos(y-xy+x)dAR is the region bounded by x+y=1 ,x+y=2 in the first quadrant.

Q: Write a definite integral which computes the area of a surface of revolution 3 1 from rotating y=-x²…

A: Topic- Application of Integration

Q: Use Property 11 to estimate the integral xxD esin x cos y dA, where is thedisk with center the…

A: We know that –1 ≤ sin x ≤ 1 and –1 ≤ cos y ≤ 1, Hence, –1 ≤ sin x cos y ≤ 1

Q: 7) Set up and evaluate the definite integral for the area of the surface generated by revolving y…

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Q: iii) Set up an integral for the area of the surface generated by rotating the curve about the…

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Q: Use either a computer algebra system or a table of integrals to find the exact area of the surface…

A: Solution

Q: Write an integral for the area of the surface generated by revolvingthe curve y = cos x, -π/2 ≤ x…

A: Given data: The equation of a curve is: y=cosx. The limit of x is: .   The expression for the…

Q: Find the surface area of revolution about the x-axis of y = 7 sin(3x) over the interval 0 < x <

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Q: The base of a lamp is constructed by revolving a quarter circle  y = (2x-x^2)^0.5  around the…

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Q: Find the area of the surface obtained by rotating the curve y = V1+ e, 0sx<1 about the X-axis. 2).…

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Q: Set up and simplify the integral that gives the surface area of revolution generated by rotation of…

A: Given; y=x-x^2, 0≤x≤1

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

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Q: Find the surface area of revolution about the x-axis of 5z +3 over the interval 1 < z < 2

A: y=5x+3 &amp; given interval 1≤x≤2As we know surface area of revolution abput x-axis from x=a to…

Q: Find the surface area generated by y = x³; x = 0 and x = 3 and is revolved on x-axis.

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Q: Find the surface area of revolution about the x-axis of y = 2 sin(2x) over the interval 0 ≤ x ≤ KIN

A: When a cut= when a curve y=f(x)  a≤x≤b  rotate about x axis then surface area of rotation Ax=∫ab2πy…

Q: 3) Write the integral that equals the area of the surface formed by rotating the curve x = 1+ 2y2, 1…

A: Recall: If the curve is given by x= g(y) ,c≤y≤d and rotated about the x-axis , then the area of the…

Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

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Q: Find the surface area of revolution about the x-axis of y = 2 sin(4x) over the interval 0 <I<

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Q: Set up and evaluate the definite integral for the area of surface generated by revolving the curve…

A: given curve y=2x over the interval [4,9]

Q: Consider a volume of a solid under the surface z = sin(x³) can be denoted as 4 2 sin(x³) dx dy i.…

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Q: Find the integral that represents the surface area obtained by rotating around the x-axis the graph…

A: To find the integral representation for the surface area under the given conditions.

Q: Find and compute the integral that represents the surface area obtained by rotating around the x…

A: We have to find surface area of revolution about x axis of f(x) in [0,pi].f(x) is given by (f(x)=y)

Q: Compute the surface area of revolution of f (x) (x + 1)z about the x-axis over 3 [0,1]

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Q: Find the surface area of the volume of revolution for the curve f(x) = In|sec x| around the x-axis…

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Q: Find the area of the surface of revolution generated by revolving the graph of = In x ,bounded by y…

A: (6) Plot the graph to find the region. The shaded area is the region.

Q: Use the WASHER METHOD to set up a (sum of) definite integral(s) that is equal to the volume of the…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Use either a CAS or a table of integrals to find the exact area of the surface obtained by rotating…

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Q: 6. Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: compute the surface area of revolution about the x-axis over the interval. y = (4 − x2/3)3/2, [0, 8]

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Q: Set up an integral to find the surface area when rotating the region defined by y=√x , 2≤x≤6 about…

A: we have to set up an integral to find surface area of given function, so

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-9x.

A: Given: y=e-9x and 0, 1 To find the surface of revolution about the x-axis on 0, 1 The formula for…

Q: compute the surface area of revolution about the x-axis over the interval. y = x, [0, 4]

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Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations y = 4…

A: Given: The region bounded by the graphs of the equations y=4-x2, y=x+2.

Q: Find the product of one of the integrals: dA 1- Sdydx 2- S SR Jty In(y) x²+y2 y = -x, x = -y where R…

A: In this problem , firstly change the order of integration .i.e, dy dx =dx dy and change the limits…

Q: Find the surface area of revolution about the x-axis of y = 6 sin(7x) over the interval 0 < x < 7

A: Here we have y=6sin(7x)  We have to find surface area of revolution about x axis in interval 0 to…