Use the transformation T : (u, v) → (x, y) with 1 1 3(u + v), y = 3(v – 2u), to evaluate the integral I = I| (3x +2y) dxdy when D is the region bounded by the lines y = x , Y = x – 2 and y + 2x = 0, y + 2x = 3. 1. I = 4

Q: Integrate f(x,y) = x+y over the curve C: x² + y²=81 in the first quadrant from (9,0) to (0,9).

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 3. Compute the inner product g (v,w) of v = + x. 2 əx and w = x.-+ 2y. Əx ay' Where the line element…

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Q: I am reallly having a difficult time

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Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

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Q: Let, T:R' → R³;T(x,y,z)=(2x+ y, y- z,2y+4z) 2. Find the rank and nullity of T.

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Q: Integrate f(x,y,z) = (x+y+z)/(x² + y² + z²) over the path r(t) = 2t i + 3t j + 3t k, 0 <a stsb. The…

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Q: 12. Use the transformation z (u + v), y = (v - 3u) to evaluate the integral ff (4x+8y) dA, where R…

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Q: Let F (x, y, z) = (x + y, x² + y², x³ + y³ + z³). Calculate JF (x, y, z) and find where F is locally…

A: To calculate the Jacobian matrix J_F(x, y, z) of the function F(x, y, z) = (x + y, x^2 + y^2, x^3 +…

Q: Use the chain rule to eX Pressdy intermsof X and Y: and t= at X=2

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Q: The transformation T : R? → R² defined by T(u, v) = (u – v, 2u – v) carries the rectangle R with…

A: Given The transformation T:R2→R2 defined by Tu,v=u-v,2u-vCarries the rectangle R with vertices 0,0,…

Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: ented square v V , (0, 1). The va + 8x² y dy)

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Q: Evaluate the triple integral 6 r32+2 LL ²²5-4 32 using the transformation u = x - 3z, v = 4y, and w…

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Q: Suppose F(x, y, z) = (ex, 2³, y² + 2) (a.) calculate V x F (b.) let C be the line segment from (0,…

A: (a.) To find: .(b.) To find: , where C is the line segment from (0, 0, 0) to (1, 2, 3).

Q: Evaluate 7. dr

A: We will use F→.PQ→ to evaluate integral

Q: Use the given transformation to evaluate the given integral, where R is the triangular region with…

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Q: Use the transformation u = y - x, v = y, to evaluate the integrals on the parallelogram R which has…

A: We need to evaluate the integral: ∬Ry-xdA using the transformations: u=y-x, v=y. Here, R is a…

Q: use the inner product = p(x)q(x)dx. to find the projection of p(x) q(x) = 5x + 2. = S'; x3 onto

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

Q: In the following exercises, use the transformation u=x+y,v=x−yu=x+y,v=x−y to evaluate the integrals…

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Q: (Give your answer in the form (*, *). Express numbers i

A: Given, the parallelogram is spanned by the vectors 7, 10 and 9, 5.

Q: Use the map G(u, v): = a = 5, b = 10, c = 3. b a y=cx u uv v+1' v+1 f (x + y) (x + y) dx dy = to…

A: By changing the variables of integration according to given map, we can find the value of given…