3 (z- i) +1 dz, - (z – i)? where C is a closed contour traversed once in the counter-clockwise direction enclosing z = i. %3D

Q: 4. (4-2x+y) dy dx = Jo J2x-4

A:

Q: xydy – (y² – 3x²) dæ = 0

A:

Q: Evaluate cosh(72) dz, C the line along the imaginary axis from to 2i. cosh(72) dz

A:

Q: D7 + D® – 2D$ – 2D4 – 7D³ – 7D² – 4D – 4) y = 0 - - - -

A: follow next step

Q: F = 5x45 i + ev6 jl and Clis the quarter of the unit circle in the first quadrant, traced…

A: Given, F→=5x45i^+ey6j^, and C is the quarter of the unit circle in the first quadrant. We have to…

Q: dæ . (x – 3)væ² – 6x + 5 Evaluate 2.

A: To evaluate the following integral

Q: *csch(2 sin 2x)cx 1. V1-4x let u= du=

A:

Q: (zy+9)8 dydr

A:

Q: use Substitution method to Schve (3メ -2Y +1)dx -(X-2Y-3)dy=o

A: The given differential equation is 3x-2y+1dx-x-2y-3dy=0.

Q: alla Find xy² R2² -dA, R= [0, 4] × [ - 2,2] x² +1

A:

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (3, -7) 21

A:

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

A:

Q: Use u-substitution for #7 xe* dx

A: Substitute:-         x2 by u then integrate

Q: AC) = -t+J At - t) sin rdt %3D OA. -t + OB. .3 -t 12 OC. OD. -t + O E. e -- 6.

A:

Q: Evaluate I C: x-axis from (0, 0) to (0, -5) and (0, -5) to (2,-5) (2x - y) dx + (x + 5y) dy.

A:

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: the origin 2 2 S (1-10²1) ² dx -1 2

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Q: se: Two different con

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Q: dw Find ду dw at the point (w, x, y, z) = (3, - 1, - 1, - 1) if w = x3y? + yz-z° and x2 + y? +z? =…

A:

Q: 2х — 1 - dx 6х + 18 x² -

A:

Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…

Q: Paragraph 12) S, dx Sx+7

A:

Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

A:

Q: 2)8 Sx' 1- x dx

A: Indefinite integration

Q: Find the centroid of the plane area shown below using integration. y²= 3x - y = x²/3 -X

A: The centroid or geometric centre of a plane figure is the arithmetic mean position of all the points…

Q: у4у? -16у +19 dy (y-2)°

A: This indefinite integral can be solved by the substitution method.