Use Green's Theorem to evaluate |. (y? – 6y) dx + (y³ + 10y²) dy where C is shown below.

Q: c) Evaluate [| 4xy where D is the portion of x + y = 2 in the 1* quadrant.

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Q: +). L x-1 dx -1x2+1

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Q: C) Find S x2e-* dx

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Q: F Só So dx dy. x2+1

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Q: I. Evaluate the following: a. (x³ + cos y + 5 dy = - 3yx²) dx b. xdy – ydx = (4x2 + y2)dy c. dx +…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Evaluate Jo (2x - y) dx + (x + 5y) dy. C: x-axis from x = 0 to x = 6

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Q: Evaluate 12 ST[-6zdy dz dx

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Q: Evaluate the to -y dxd

A: Given that, the integral is ∫01∫01-y2x2+y2dxdy. Obtain the value of ∫01-y2x2+y2dx.…

Q: (x²y – 2ry) dy dx

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Q: Evaluate -42 (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) X

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Q: .2 dx Jo (9 + x²)2

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Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: Find if y = (x² – 1) (x³ + 2). dx

A: We expand the given expression and then use power rule to find the derivative.

Q: Calculate (2x+3y+z)dV where = [1,2] x [-1,1] × [0,1] A. 0 B. 1 C. 4 D. 7

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Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: . Solve the first order equation (3z²y + 2ry)dx + (x³ + x² + 2y)dy = 0.

A: Solution

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from x = 0 to x = 2

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Q: Calculate the following integrals a) S .3 dx;u = x³ – 1 | Vx3-1 3x b) S dx; u = e3x +1 e3x +1 c) S *…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Transform each of the following wffs into a full DNF if possible, explain your steps. (a.) (A v B) A…

A: To convert a well-formed formula (wff) into a full disjunctive normal form (dnf), we perform the…

Q: Evaluate (2xy + y3 + 8x)dx + (x2 + 3y²x + 6y)dy (2.0) (1,1) Select one: O a. 6 O b. 8 O C. 5 O d. 7

A: Given :                   ∫(1,1)(2,0) 2xy + y3 + 8x dx + x2 + 3y2x + 6y dy

Q: Find S x² + vx – 2 dx

A: We need to evaluate the following integral.

Q: 2. Find b such that dx 1+x2 3

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Q: Find f√x² + y² +1 dx dy, where R is defined by x² + y² = 0 and y >= 0. R

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Q: Find dy for y = (4x +2)2. dy = (Simplify your answer.)

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