16) Consider the oriented curve C, boundary of a region D, given by C = C₁ UC₂, where C₁: y=x² y C₂: y = 8-2², as shown in the figure. An expression that calculates the value of ya³ da + 2ª¹dy corresponds to: C₂ A) - .* 32²y dx dy C = OD BIL B) 3x³y dy dz C) 3x³ dx dy D) [3x²³ LP 3x³ dy dr C₁ x

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A: Given:-             Let F→x,y=e2yi→+1+2xe2yj→ (a) show F is conservative. (b)compute  ∫cf¯.t  ¯ ds…

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A: Solution-(a) the path of integration has the length L=4π Upper bound M for the function =1z2+1;z=2…

Q: a) Use polar coordinate to evaluate I √x² + y² dA R where R is the region bounded by the circle z² +…

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Q: B7. Refer to the shaded object in Figure QB7, y = -2x² +2 Part B: Determine: 1 y a) the area for…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

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A: According to our answering guidelines we can answer 3 subparts at a time, rest you can repost later,…

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Q: ²²-i)² dx 2³+dz when the contour C is the circle |z − 21 = 5 +4 1 Z- COSZ Cosz, dz when the contour…

A: According to the guidelines only three subparts should be answered. Therefore to answer the rest of…

Q: y = x³ ve x = y² eğrilerinin kesişim bölgesinin alanı aşağıdakilerden hangisidir? A) B)금 E) 12

A: Given,            y=x3x=y2   As we know, If we have two curves  y=f(x) and y=g(x) and f(x)&gt;g(x)…

Q: 2) The region is defined by y= sin x, y = 0, x= 0, x = T. Rotate the region about the: a) x-axis b)…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: Find the area oF the loop OF the given curve. 2.y==x°C1-x)*

A: Using the double derivative in Cartesian coordinates.

Q: b) Let D be a region bounded by a simple, closed, positively oriented curve C. Prove: (200, ±√2) √…

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A: Given that , y=6-x , 4≤x≤6 find the area of the surface obtained by rotating the curve around the…

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Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: aS) A Graph the curve Y=-2x (x - 4)x + 6)(N - 2) between the value of then find the area of the…

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Q: 6y dA, R is the quarter-disk in the fourth quadrant enclosed by the curves r+ y = 16, r = =0, and y…

A: Explanation of the answer is as follows

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Q: 1. Region R is bounded by the given curves. (i) Sketch R and label its boundaries. (ii) Indicate the…

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A: We have to evaluate:∫C8xy6dsHere C is the right half of the circle x2+y2=4.

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Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: Find dyldx for the following equation: 2x+ y -9y+9=0. A) dy dx 2-2y В) dy dx 9-2y 2 C) dy dx 9-у 1…

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