7. Set up the integral needed to find the exact area of the surface obtained by rotating the given curve about the x-axis. DO NOT EVALUATE THE INTEGRAL. Compute any necessary derivatives but the integral does not need to be simplified. t3 1 x = 4Vt, y = 1

Q: The area of the surface obtained by revolving the curve y = x3 for 1<x<8 about the y-axis, is given…

A: Surface area obtaining by x=f(y) from x=a to x=b is about y-axis given in step 2.

Q: Set up a (sum of) definite integral(s) that is equal to the arc length of the portion of the curve y…

A: The length of the curve y=f(x) between the limits x=a to x=b is given by; L=∫ab1+dydx2dx

Q: 3. Set up an integral to find the surface area generated when the given curve x = where 0<t < 1 is…

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Q: AIS. 4. Compute the area of the surface formed when f(r) = 2 + cosh(r) between 0 and i is rotated…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Set up an integral to find the area of the surface that is obtained by rotating the curve y = V4 –…

A: Here, y=4-x2, 0≤x≤1 is positive and has continuous derivative on 0≤x≤1. So, the surface area of…

Q: Find the area of the surface generated by e + e -y revolving the curve x = 2 0sys In 6 about the…

A: To find the surface area generated by revolving the curve x=ey+e-y2,0≤y≤ln6 about the x-axis. We…

Q: Evaluate the integral / (2x + 15y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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

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Q: Consider the curve defined by the equation xy=25. Set up an integral to find the length of curve…

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Q: 1 8y² = x² – x* , 5x< curve segment is %D - rotated about the x-axis. Calculate the surface area of…

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Q: 1 1) To find the exact area of the surface obtained by rotating the curve y = 2, 0<x < 12 about the…

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Q: Evaluate the integral (+ 2) dz where C is the line segment from the origin to the point 1+ 2i.

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

A: we use integration formula for area of surface rotating about x-axis..

Q: Consider the curve segments: 1 S1: y = x from x =to x = 4 and %3D 2 1 S2: y = Vi from x = - to x =…

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Q: Consider the curve segments: S1: y = x from x = 1 to x = 2 and 1 S2: y = Vx from x =to x = 4. Set up…

A: Let's find.

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

A: Write the integral that equals the surface area of the given curve rotating about x-axis

Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

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

A:

Q: 3. Suppose the curve x = t³ – 9t, y = t+3 for 1 <t < 2 is rotated about the x-axis. Set up (but do…

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Q: 1. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A:

Q: Set up an integral to find the surface area generated when the given curve x = t3,y = t2 where 0 ≤t…

A: The curve is given as , x=t3 , y=t2  where 0≤t≤1 find surface area when curve rotated about the…

Q: Consider the curve segments: 1 S1: y = x from x =to x = 4 and S2: y = Va from x = - to x = 16. Set…

A: Given :S1 : y=x2 from x =12 to x=4S2: y=x from x =12 to x=16

Q: 2) Use the surface area formula: S = 2ny 1+ () dx to find the surface area y = x, where 0 <x <1 of:

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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: Set up an integral for the area of the surface generated by revolving the given curve about the…

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Q: Evaluate the integral [(4x + 15y)da + (6x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

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Q: Consider the following curve. y = x³, osxS 5 Set up an integral in terms of x that can be used to…

A: The surface area of revolution about the x-axis is: S=2π∫abf(x)1+f'(x)2dx If the function is,…

Q: Calculate the integral | (2x + sin y) dx + x cos y dy 7, where L is any curve from the A(0,0) to B (…

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Q: Consider the following curve. y = x, 0sxs 3 Set up an integral in terms of x that can be used to…

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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 an integral for the length of the curve. y = Vi-x7, -sxs 1/4 4+ 49, 12 dx -1/4 4- 4x7 + 7x6…

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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: Use an appropriate change of variable to evaluate the double integral: y- x cos y +x d A, R where R…

A:

Q: The arc-length of the curve y= / ycos(4t) dt, for 0<x<- 8. 0. is given by which of the following…

A: we have to find the length of the curve

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: Evaluate the integral | (2x + 9y)dx + (21x – y)dy along the parabolic arc y = x from (0,0) to (1,…

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Q: Find the area between the curves y=e−0.2xy=e-0.2x and y=1.6x+1y=1.6x+1 from x=0x=0 to x=4x=4.

A: Given query is to find the area under the curve

Q: Which ONE of the following integrals correctly represents the area of the surface of revolution…

A: giveny=ln(x5)rotation about x-axisA=∫152πyds

Q: 3. Set up an integral to find the surface area generated when the given curve x = where 0 <t < 1 is…

A: x=t3,y=t2      o≤t≤1    Given

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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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: If the curve y= from (0, 0) to (3,9) is rotated about the x-axis, the integral that represents the…

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Q: (5) Obtain the integral curve for dy +y cotx = e*cscx passing through the dx point (0, 0).

A: We have to solve the given differential equation

Q: Evaluate the line integral 11y dy over y = x for 0 < x < 3. (Use symbolic notation and fractions…

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Q: 3) Find the area of the surface that results from rotating the curve Y = sin X, 0<X< 1 about the X…

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Q: 3. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A: 1st we need to convert the curve in x=f(y) form and corresponding limits for y , Then use given…

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

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

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