1 an 1 Use the transformation u = 2x+ y, v=x+ 3y to evaluate the given integral for the region R bounded by the lines y= - 2x+2, y = - 2x + 4, y = - d y = -*+1. [[(22 +7xy + 3y2) dx dy R I(2x? + 7xy + 3y2) dx dy =O R (Simplify your answer.)

Q: Evaluate f(x, y, z) dV for the function f(x, y, z) = xz² and region B = [0, 3] × [5, 7] × [4, 5].

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A: Suppose L is the length of the line. Then, the x-coordinate of the centroid of the line is…

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A: Consider the given: R=x,y:x+y≤2x=u+vy=u−vA=111−1=−1−1=−2=2

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Q: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

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Q: SLo(xy) dA where R is bounded by 9x2 + 4y² = 36 %3D Use the transformation: x = 2u and y = 3v

A: The given region R is: 9x2+4y2=36...(1) To use the transformation: x=2u,y=3v So, equation (1)…

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Q: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x + 56. Use the…

A: The region is bounded by the graphs fx=x2 and gx=-x+56. We have to find the centroid of the region.

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Q: Suppose F(x,y)=. Use Green's Theorem to calculate the circulation of F around the perimeter of the…

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Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

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Q: f(y) { 2ye-y^2 , y > 0         { 0, otherwise Find the G(U) transformation such that if U has a…

A: The probability density function of y f(y)= y>0U~U(0,1) Using FormulaCumulative distribution…

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Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

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Q: CD has coordinates C(-8,-2) and D(-4,-12). determine the coordiantes of C'D' if (x,y) -> (1/2x,1/2y)…

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Q: Use a substitution of u = r to integrate : dr.

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Q: Plot the function f(x, y) = x² – y² over the square region bounded by the lines y =x - 2, y =x+ 2, y…

A: Given the function fx,y=x2-y2

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A: Given: A two-form on ℝ3; ω=e6x+zdy∧dz+e-ydz∧dx+e4x-zdx∧dy. A smooth function, ϕ:ℝ>02→ℝ3 defined…

Q: Check cosh(xz)(z dx + x dz) for path independence. Does cosh(xz)(z dx + x dz) have path…

A: To verify whether the function cosxzzdx+xdz is path independent or not…

Q: a(x,y) d(u,v) Evaluate the Jacobian for the change of variables X =, =u²cos(v) and y =usin (v).

A: Topic : calculus