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: 35. f(x, y) = x² + 2y² – x; R is the disk x? + y? < 4.

A: fx,y=x2+2y2-x which is bounded by R, R:x2+y2≤4, where R is a disk Partially differentiating fx,y…

Q: = + E (0 < x < L,0 < t <ox) L Ot u (0, t) %3D 0, и(L,t) %3 0, и(х,0) — А, и (т,0) %3D0.

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Q: f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball x² + y² + z² 2.5

A: Here we will use cylindrical co ordinate system to find value of integral  By using above figure…

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Q: u = f(x,y) and v = g(x,y) ? %3D %3D

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Q: 2. Evaluate f. (y²dx + x?dy) where C is the triangle with vertices (1, 0), (1, 1), (0, 0).

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Q: If C:7() = (1+t,1–-P), -1sts2 and g(x,y)=x²y+x+y+2, then Sg,«.) dx + g,k.y) dy = %3D C 22

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Q: a) What is the dimension of {(x, y) E R² : x + y = 0}?

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

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Q: Find Cx(x,y) if Cx(x,y) = 2x2 + 7xy - 9y2 + 4x - 9y - 6 Cx(x,y) = ?

A: Let's find.

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Q: Find Duf at P. f(x, y, z) = 4x'y°z?; P(1, – 2, 1); u = - 2. Duf

A: The objective of the question is evaluate the directional derivative at a given point.

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Q: 26. ƒ(x, y) = ye*; R is the rectangular region with vertices (0, 0), (In 2, 0), (In 2, 3), (0, 3).

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Q: Evaluate p xy*dx + a*dy, where C is the rectangle with vertices (0,0), (2,0), (2,3), and (0,3)

A: *Concept:- Use Green's theorem.

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Q: dp For p(q).= q¯³, dq -3 dw For w(u) = u7, du %3D %3D

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Q: Evaluate ſ √x² + y²dxdy over the triangle with corners (0,0), (4,4), and (4,0) using x = u, y = uv.

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Q: dw dw Find ду and ду at the point (w, x, y, z) = (9,3,1,1) if w = x²y? + yz- z³ and x2+y² +z² = 11.

A: The solution of the problem is given in the next steps.

Q: Evaluate O xy°dx + x²dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

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Q: II. (²z + y²z) ds S is the hemisphere x2 + y? + z² = 9, z

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Q: p ry*dx + x*dy, where C is the rectangle with vertices (0,0), (1,0), (1,5), and (0,5) Evaluate

A: We will convert this line integral to surface integral using greens theorem

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

A: The solution is given by using greens theorem as follows

Q: Evaluate II, (z*y +) dz dz dy, where D = [0, 1] × [0, 1] × [1, 2]. %3D

A: Here we have to find the integration if triple integrate: ∭x2y+1zdzdxdywhere D=0,1×0,1×1,2Thus it…

Q: Exercises 41 and 42, evaluate (y – x) dx + (2x + 5y) dy. 41. C: line segments from (0, 0) to (2, –…

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Q: Evaluate p xy da + a dy, where C is the rectangle with vertices (0,0), (3,0), (3,6), and (0,6).

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Q: S. Re{z²}dz; C is the square with corners 0, 1,1+i, i. [1+i]

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. v), y = (u + v) X = -

A: The formula for the Jacobian is: ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v

Q: If z = x + y, x = 2t, y = 3t, then %3D %3D 1 5 II

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Q: Find the Jacobian d(x, y) / d(u, v) for the indicated change of variables. u- v), y =u + v) X = -

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Q: - {z,y, 2)| 2 2= > 0} //| dpdød0 set Consider the 3D domain W = Calculate | a2 + y? + z² d(x, y, z)…

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Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

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Q: If C is the square with vertices (+1, ±1) oriented counter- clockwise, then -y dx + x dy =

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Q: Find the value of o(4x + y)dy - rydy where C is the path around the triangle in the counterclockwise…

A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = xy + yz + xz

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Q: We are given w = 2yln(y+2z)+x2, where x=b√c, y=c-a2, and z=ab+1. Find the following ∂w/∂a at the…

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Q: Evaluate p a?y°dx + x°ydy 2,2 3 counterclockwise around the square with vertices (0, 0), (1,0), (1,…

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Q: 9. f(z) = e'n/4z %3D

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Q: Find z and z, Zy. z = 2x*y5 !! %3D Zy %3D × | > N

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Q: r(2,4) Sa (2y+x) dx +(3x– y)dy} along the straight line x-2t and Evaluate J(0,3) y=P+3.

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Q: Sc (x cos x - y) dx + (x – e") dy; C is the square wit vertices (-1, 1), (-1, 0), (0, 0), and (0,…

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Q: aw Find ди dw. and if w = x³ + In (-) + y, x = u? dv -+ 5 and %3D wwww y = 3v + 5u and point…

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