Suppose that f(x, y) and the region D is given by {(r, y) | 1 < # < 2,1 < y < 4}. D Then the double integral of f(æ, y) over D is /| f(x, y)dædy =

Q: Find the value of the line integral  ∮ C (2*y + e^x) dx + (ln(y) + 8*x) dy, where C is a closed path…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. The Green's theorem…

Q: Evaluate the line integral 2'y dx +a/y² +1 dy for C : r(t) = (VE, t?),0 < t < 1 and then repeat with…

A:

Q: Q3) Calculate the following integrals over the given C curves by using the Cauchy integral formula.…

A: Part (3):-  Given information Sub-part (a):- ∮e-zz2+π24 dz        C:z-i=1  circle Sub-part (b):-…

Q: 6. Evaluate the triple integral f, x?yz dV, B = {(x, y, z): - 2 < x<1,0 < y< 3,1<z<5}

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Q: Suppose that f(x, y) = 3x + 1y at which {(x, y) | − 5 ≤ x ≤ 5, -5 ≤ y ≤ 5}. D Then the double…

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Q: Evaluate the line integral ry dz for C : r(t) = (e , et+1)", te'), 0 <t<1 and then repeat with -C in…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Write down the new limits of integration for the integral -1 -1-y IIL" S(7,4, 2) dz dy dæ if the…

A: As per given tripple integral  0  ≤  z  ≤  (1 - y)  x2  ≤  y  ≤  1  -1  ≤  x  ≤  1   Thus, curves…

Q: 2)Evaluate ex dA , Ris bounded by y = x2,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: 4. Set up the iterated double integral equal to the surface area of the portion of R(u, v) = (1-u³,…

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Q: Evaluate (x + y)ds where C is the straight-line segment x=t, y = (4 – t), z = 0 from (0,4,0) to…

A: We have to find the given line integral.

Q: Suppose that f(x, y) = 2, and D= {(x, y) | x² + y² ≤ 4}. Then the double integral of f(x, y) over D…

A: Given that f(x,y)=2 we have to find the double integral ∫∫Df(x,y)dxdy where D is D={(x,y)|x2+y2≤4

Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: Flxyy) de dy is an integral orer what region?

A:

Q: The graph of fis shown. y y= AX) 10 10 20 30 40 Evaluate each integral by interpreting it in terms…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Suppose D is the region in the plane bounded by the lines x + y = 0, x +y = 3, x – 2y = 0, and x –…

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Q: Let F(x, y) = (2xey ,x + x2ey} and let C be the quarter-circle path from A to B in Figure 18.…

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Q: Evaluate the integral ∬R(x2+y2)dxdy, where R is bounded by the lines y=x, y=x+a, y=a, y=2a (a&gt;0).

A: The region is bounded by  y=xy=x+ay=ay=2a We have to evaluate ∬R x2+y2 dx dy.

Q: If the change of variable |ə (x, y) d(u, v) | v v³ (²) = (²+²) u at the point where (x, y) = (2, 3)?…

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Q: linean trensformabe which af the Pollowing ý a Pixiyiz) =(xyt, x+y, x+2, YtZ) PXIYA) =(2x,2y 12Z,…

A: Note:- 1) Due to our guidelines we can solve only 1 question. 2) In question 1) there is a…

Q: Let D be the region bounded by the parabola y = x2 and the curve y = sin x, and let P represent a…

A: If the input of the function is more than one, such functions are called multivariable functions.…

Q: 3)Evaluate || Vy2 + 1dA , Ris bounded by x = 4 – y² ,x = 0 R

A:

Q: 3- Since the D x=1 line is a region bounded by the x-axis and the graph of the y= x^(1/2) function,…

A: y = x^(1/2) is a parabola with vertex (0,0). Draw it and solve it.