Verify Green's Theorem by evaluating both integrals an aM dA y² dx + x² dy = |/ əx ду for the given path. C: square with vertices (0, 0), (8, 0), (8, 8), (0, 8) dx + ON dA = ду

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: The figure below shows the expression for the x-centroid of line L. Suppose length L is 10 cm and…

A: Suppose L is the length of the line. Then, the x-coordinate of the centroid of the line is…

Q: If the substitution u = √x + 1 is made, the integral 3 A S u² u² - 1 du B du 3 2u²2 u² - 1 √ √x+1 dx…

A: We solve the given problem by using the substitution method.

Q: function fo) = 7X1+10x10x3_4 Qn Antiderivative of fo) is F(x) = Axn+ Bxm, CxP+Dx: A= 710 %3D where…

A: Solve the following

Q: Evaluate the integral -3-2s ds. V-3-2s ds %3D

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Q: Find the general solution u(x,y) of: uxx - 3ux + 2u = 0. XX

A: Given partial differential equation is  ----------- (1)              where  ,    and…

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: Let r(t) =ti +t³j +tk The normal component of acceleration is an = 6t/2/V9t4 + 2 а. b. an= 4t/2/V9r*…

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Q: Let C be the boundary of a rectangle with vertices (0, 0), (-1,0),(-1,5) and (0, 5). Then ve dx +…

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Q: 3) Express aw/ar and aw/as in terms of r and s if w = x +2y+z², x = 5, y = r² + Ins, z = 2r

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Q: Find the general solution u(x,y) of: uxy : 2y. =

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Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

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Q: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x + 56. Use the…

A: The region is bounded by the graphs fx=x2 and gx=-x+56. We have to find the centroid of the region.

Q: Calculate the length of the astroid of x2/3 + y2/3 = R2/3 for R = 2. -R R -Rt +x R

A: To calculate the length of the asteroid of

Q: Evaluate e [ f(x, y, z) ds, where f(x, y, z) = 2 + 2y + (z + x) and C is the line segment from (2,…

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Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

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Q: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi –…

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Q: Substitute r = 1 into + p(z)y=f(z)y and show the result is linear. Write your answer in linear…

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Q: Use a substitution of u = r to integrate : dr.

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Q: af Let f(x, y) = x³y + 8. Compute (1, 2) and -(1, 2). ax ду

A: Given: fx,y=x3y+8

Q: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyx, g(x, y, z) = x²yz, U = x²yi –…

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Use Linear Approximation to estimate the change, Az, in z = 8x2 + y? as (x, y) changes from (2, 3)…

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Q: дz Find and əx дz ду' yz + x ln y = z²

A: Given query is to find indicated partial derivatives.

Q: 3x + 2 dæ, Hint: Remember that 4 = 4 + . = +. A+B 4. b) Integrate %3D

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Q: And a. he minor of the element in the i li, ro Column of ass the deferminant of A, find

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Q: Show every detail of your solution. Differential equatioens. siny dx + (x - sin? y)dy3D0

A: The given differential equation is: sin y dx+(x-sin2y)dy=0⇒sin y dx=-(x-sin2y)dy⇒dxdy=-(x-sin2y)sin…