Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with vertices (2, -1), (2, 1), (-2, 5) and (-2, -1) with positive orientation.

Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

Q: Evaluate O xy?dx + a°dy, where C is the rectangle with vertices (0,0), (6,0), (6,3), and (0,3)

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Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

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Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Q7 Show that CX,y) =e is Condinuous at co,0)

A: The given function is:  fx,y=e-x2+y2 The given point is 0,0

Q: x y 11. Use Green's theorem to evaluate O In(1+ y) dx –- dy , where C is the triangle with vertices…

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Q: Evaluate J₁ 1 E x² + y² + z² x² + y² +2²= 25 in the first octant. dV, where E lies between the…

A: Here we need to use spherical co ordinate system to find value of integral  Relation between…

Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: 14. Evaluate o 4y dr + 3r dy, where C is the trapezoid with vertices (0,0), (2,0), (6, 2) and (0,…

A: The solution are next step

Q: Use Green's Theorem to evaluate (y? tan- a?) dx + (3.xy+ 4x – In(y² + 4)) dy, where C is the…

A: We need to evaluate integral.

Q: 7. Evaluatexyddx+e*dy where C goes along the x-axis from (0,0) to (2,0) and then along the parabola…

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Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: - Evaluate the follwoing | r" exp(ax")dx where a + 0 and m+l = 1, 2, 3, ...

A: Given integral is, ∫xmeaxndx Substitute, u=am+1nxm+1dudx=m+1am+1nxm+1dx=1m+1am+1nxm+1du Then,…

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &3, x2-y2=3 &4 Where u=xy and v=x2-y2

Q: Compute dy/dx using the chain rule in formula. State your answer in terms of x only.  y = u3>2, u…

A: Given equations - y = u3+2           .....(1)                                                  In…

Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: am dA y² dx + x² dy = / / ( - əx ду for the given path. hC: rectangle with vertices (0, 0), (2, 0),…

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Q: Find the absolute maximum and minimum values of f(x, y) = 3xy−6x−3y + 7 on the closed triangular…

A: Find out the absolute maximum and minimum values of  f(x,y)=3xy-6x-3y+7 for the maximum and minimum…

Q: Calculate the “n” of the DE with the given 6y^2dx-x(2x^3+y)dy=0

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Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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Q: 4. Use Green's Theorem to evaluate | xy dx + (1 – xy°) dy where C is shown C below. y (1,4) (-1,2)…

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Q: 4. Determine the c, and c2 so that the y(x) = c,e-* + cze8x + sinx that will satisfy the initial…

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Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: Find dy/dx if y = x^3/2 by using the Chain Rule with y as a composition ofa. y = u3 and u =…

A: a) y=u3 and u=x     dydu=3u2anddudx=ddxx       =12x-12 So, dydx=dydu×dudx      =3u2×12x…

Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: Evaluate xy dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,1), and (0,1)

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: a When reduced to a linear DE of order one in z, the Bernoulli's equation dx becomes dz A + z( − 1)…

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Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

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Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

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Q: Find the general solution of this DE using INSPECTION. dnda + +(x? t y?)dx = 0 2 aycdly

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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Q: E). f(x, y) = sen?(r2 – 0²) + In(r0 + 0), r = Vx2 + y² 0 = arctan con -

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Q: Obtain the Solution x, y > 0, xy > 1 of the PDE 2y on the x+y 1 Uxy such that u = x+y 0, ux…

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Q: 8. Evaluate the line integral fx'dx + xe 'dy where C is the closed path along the triangle in the…

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Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: 1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1,…

A: Given: The function with two polygonal paths in space joining the origin to the point (1, 1, 1).…