Show that the form under the integral sign is exact in the plane and •(2,2) evaluate the integral / e--" (x dx + y dy). (-1,–1) NOTE: Enter the exact answer. (F.), (F2),

Q: Please evaluate the following line integral: Sc y? dx +2xy dy By parameterizing C as the line…

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Q: Determine the value of the integral Integral sign: ((z^2 + r^2)^-3/2)x((2r)dr)

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Q: Evaluate the line integral f y(tan x + x sec² x) dx + x tanæ dy + dz once around the circle x² + y²…

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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: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

A: The given line integral is ∫c-ydx+xdy along the curve c: y2=6x from (6,6) to (0,0)

Q: .2 (3 – z)(3z + 1) dz

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Q: Evaluate the line integral -ydx + xdy along the curve C: = = 21x from (21, 21) to (0,0). %3D NOTE:…

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Q: Use symmetry to evaluate the double integral. Ja+ (1 + x8 sin(y) + y sin(x)) dA, R= [-π, π] x [-π,…

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Q: Find the line integral of ƒ(x, y) = yex2 along the curve r(t) = 4t i - 3t j, -1 <_ t <_ 2.

A: Given: f(x,y)=yex2 r(t)=4ti-3tj -1≤t≤2 From r(t)=4ti-3tj x=4t,y=-3t Differentiate with respect to…

Q: Use Green's theorem in order to compute the line integral £ (x – 3)³ dy – y³ dx where is the circle…

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Q: The surface area of the solid generated by revolving the straight line 2y = x+1 bounded by x-1, x 3…

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Q: Set up an iterated triple integral equal to | = √√3 √3-x² √√30 x²+y² 3 √2-√4-x²-y² 2y dz dy dx…

A: The given problem is to set the given triple integral in Cartesian coordinates to convert into the…

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: Evaluate the line integral -ydx+ xdy along the curve C :y = 12x from (12, 12) to (0,0). NOTE: Enter…

A: In this question , we can find the given line integral.

Q: Evaluate the double integral (x +y)² sin(x – y) dA for R, which is square with the vertices (0, 1),…

A: Consider the given integral and construct a diagram based on the given conditions.

Q: О 3D 2х — у, 1<x<2 -

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Q: The path C is a line segment of length 13 in the plane starting at (4,5). For f(x,y)=5x+12y,…

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Q: Use substitution to find the indefinite integral. 2. zy5z 5z²-8 dz 2. - 8 dz =|

A: The given integral is: I=∫z5z2-8 dz

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: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: Evaluate the integral (1+ etane) Sec?0 de

A: The given integral is, I=∫0π41+etanθsec2θdθ Let us solve the given definite integral using the…

Q: *0 = x = 0, y = 1, x = y about the line y = 1 can be computed using the method of disks or washers…

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Q: Evaluate the line integral - -ydx + xdy along the curve C : y? = 3x from (3, 3) to (0,0). NOTE:…

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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: Evaluate the following line integrals in the complex plane by direct integration (not using…

A: Complex

Q: What is the integral of the constant function f(x, y) = 5 over the rectangle [-2, 3] x [2, 4]?

A: Given:            f(x, y) = 5   over rectangle -2, 3×2, 4

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: The amount of work that a force field does on a particle as it moves along the boundary of a…

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Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: Work done= Force * distance                     =(force due to Weight)* distance

Q: S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z?)dy + (3z² – 3xy + x² + 2yz)dz

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Q: Evaluate the line integral, where Cis the given curve. xyz? ds, C is the line segment from (-1, 4,…

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Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

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Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: 4) Write the integral to calculate the outward flux through F = (-yx2, xy,-z) across the sphere with…

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Q: Evaluate the line integral. 7ydx + 6z dy + x dz, r(t) = (2 +t,,1?) for 0 <t<1 (Give an exact answer.…

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Q: Show that the integral is independent of the path, and use th Fundamental Theorem of Line Integrals…

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Q: Evaluate be (x² + y²) ds, C is the right half of the circle with radius 3 centered at (0,0). Hint:…

A: To evaluate    ∫Cx2+y2ds where C is the right half of the circle with radius 3 centered at 0, 0.…

Q: Find the are length of the curve y² = 3x between the from x=0 to x=9 ! Use integral approximation!…

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Q: Integrate f(z) = 1 counterclockwise around the unit circle, using 28 – 4.4 Cauchy's integral theorem…

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Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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Q: 2. Set up the integrals for the work required to pump the water in the drum shaped solid to the goal…

A: set up the integral for w9rk requireded to pump the water in the drum shaped solid to the goal line

Q: Evaluate the iterated integral. 3 (2z fIn(x) '3 xe-Y dy dx dz Jo

A: ∫13∫02z∫0ln(x)x e-y dy dx dz

Q: Express the length L of the curve r = sin3(0), 0 < e < as an integral but do not evaluate it. /7 de

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Q: 2 V2y-y2 Evaluate the integral x²+ y²dzdydx by using cylindirical coordinates.

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: d) Use line integral method to evaluate F(x, y)• dř ,where R 1 F(x, y) = (3x y°i + 4xy² j) and M, N,…

A: The graph of curves y=x2, y=x is as follows The yellow colored region is region R

Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…

Q: Evaluate the line integral -ydx + xdy along the curve C : y = 3x from (3, 3) to (0,0). NOTE: Enter…

A: We have to find the line integral ∫C-ydx+xdy along the curve C: y2=3x from (3,3) to (0,0)