se the given transformation to evaluate the integral. J 6z + 3ydA, where Ris the parallelogram with vertices - (u + v). y - (2u – v).

Q: Use the transformation u = 3x + 4y, v=x+4y to evaluate the given integral for the region R bounded…

A: Formula Used: ∫∫Rf(x, y) dxdy=∬f(u, v) J du dv

Q: Use the given transformation to evaluate the integral. 7x2 dA, where R is the region bounded by the…

A: x=5u, y=6vThen 36x2+25y2=900 becomes36(54)2+25(6v)2=90090042+900v2=900⇒…

Q: Evaluate the iterated integral J"]T 0, 0, zr dz drde. a. е. 8 16 f. 4 c. g. d. 2n h. b.

A: given=∫02π∫01∫01-r2zrdzdrdθintegrating=∫02π∫01[z2r2]01-r2drdθ=∫02π∫01[(1-r2)r2-0]drdθ=12∫02π∫01(r-r3…

Q: Evaluate the line integral , F. dr where F = (-4 sin x, –3 cos y, 10xz) and C i: the path given by…

A: Given that F→=-4sinx, -3cosy, 10xz and C is the path given by r→t=2t3, t2, -2t for 0≤t≤1 We have to…

Q: Calculate the iterated integral. r5 CT/2 (y + y2 cos(x)) dx dy -5Jo 120

A: Given query is to find the value of the individual integral.

Q: Use the given transformation to evaluate the integral. 8y2 dA, where R is the region bounded by the…

A:

Q: Evaluate the line integral , F dr where F (3 sin x, -5 cos y, xz) and C is the path given by r(t) =…

A:

Q: Use the given transformation to evaluate the integral. || 5x? dA, where R is the region bounded by…

A: Solve the double integral bounded by ellipse,using Jacobin transformations

Q: Use the given transformation to evaluate the integral. 3xy dA, where R is the region in the first…

A:

Q: Evaluate the line integral along the curve C. (xz+2) ds, C is the curve r(t) = (-6-2t) i + tj- 2tk,…

A:

Q: Evaluate the line integral by the two following methods. pxy dx + x?y³ dy C is counterclockwise…

A: Sketch the graph of the triangle with vertices points (0, 0), (1, 0), and (1, 4) as shown below:…

Q: Use an appropriate transformation to eval- ate the integral /, sin(1 + 9y°) drdy 1 = I D -hen D is…

A:

Q: Use the given transformation to evaluate the integral. 7x2 dA, where R is the region bounded by the…

A: Given : R is the region bounded by the ellipse 9x2+25y2=225 given transformation x=5u,y=3v We want…

Q: Use the given transformation to evaluate the integral. || 2 Y dA, where R is the parallelogram…

A: Given, ∫∫Rx-4y6x-ydA Where R is the parallelogram enclosed by the lines x-4y=0,x-4y=2 and…

Q: Use the given transformation to evaluate the integral. || 2y dx dy, u=X+ y, V = - 2x+ y R where R is…

A: short summary:  Firstly we can draw a parallelogram bounded by the given lines and find intersection…

Q: Use the symmetry to evaluate the double integral given below.

A: Given∫∫R(2+x2y)dA  R=[0,1]×[-1,1]

Q: Use the given transformation to evaluate the integral. 4xy dA, where R is the region in the first…

A: We will find out the required value.

Q: Evaluate the line integral along the curve C. J (3x - 2y) ds; C is the line segment r(t) = (2t,t)…

A:

Q: Use the given transformation to evaluate the integral. I| 7(x + y) er - y² da, where R is the…

A: Given that, the rectangle is enclosed by the lines x-y=0,x-y=5,x+y=0 and x+y=10. And also given…

Q: Use Green's Theorem to evaluate the line integral of F = (x°, 6x) around the boundary of the…

A:

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

A: To find the integral using given transformation .

Q: Use the given transformation to evaluate the integral. 6 sin(81x2 + 25y2) da, where R is the region…

A:

Q: a) By using the change of order evaluate the integral e dxdy 2in3 Jin 3 60 y/2 b) Use the polar…

A: To change the order of integration we take small strip parallel to y axis

Q: Use the given transformation to evaluate the integral, where R is the parallelogram bounded by the…

A:

Q: Use the given transformation to evaluate the integral. 3x dx dy, u = x+ y, v = - 2x+y where R is the…

A: To evaluate the double integral using change of variable follow: Determine the region under a given…

Q: Use the transformation u = 3x + y, v=x+3y to evaluate the given integral for the region R bounded by…

A:

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

A: I am solving from step 3 We know that equation of line passing through points x1,y1 and x2,y2 is…

Q: Use the transformation u = 2x + y, v = x + 4y to evaluate the given integral for the region R…

A:

Q: se the given transformation to evaluate the integral. 3xy dA, where R is the region in the first…

A: We have to evaluate the integral bounded by given lines and hyperbola curves.

Q: Evaluate the triple integral -6 (x – 3)³ (y + 13)² (z – 2)4 - dz dy dx 8 49 625 3 by using the…

A:

Q: Use the given transformation to evaluate the integral. 8xy dA, where R is the region in the first…

A:

Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (fg) = (7x2,8y?) and…

A:

Q: Q2/(a): Evaluate the double integral , 3xy dA over the rectangle dA = dydx} R {(x, y): -3 x< 2,…

A:

Q: Use the given transformation to evaluate the integral. 8xy dA, where R is the region in the first…

A:

Q: Use the given transformation to evaluate the integral. 15) x = 6u, y = 9v, z = 2w; x2 y2 z2 dx dy…

A:

Q: Use the given transformation to evaluate the integral. (x – 6y) dA, where R is the triangular region…

A: Transformations: x=5u+vy=u+5v Vertices are (0,0), (5,1) and (1,5) By these three points we get the…

Q: Find the line integral of f(x,y) = y e* along the curve r(t) = - 5t i – 12t j, - 1sts0. The integral…

A: Use parametric to integration

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

A: Let us consider the integration I=∫R∫f(x,y)dxdy Change the variable to x=f(u,v)y=g(u,v) The integral…

Q: Use the given transformation to evaluate the integral. || 10y2 dA, where R is the region bounded by…

A: Given the given integral is ∫∫R10y2dA, Where R is the bounded by the curve xy=2, xy=7, xy2=2 and…

Q: Find the line integral of ƒ(x, y) = sqrt(y)/x along the curve r(t) = t3i + t4j, 1/2&lt;=t&lt;= 1.

A:

Q: Evaluate the line integral , F. dr where F = (3 sin x, -5 cos y, xz) and C is the path given by r(t)…

A: To determine the value of the integral.

Q: Evaluate the line integral , F. dr where F = (– sin x, –3 cos y, 5xz) and C is the path given by…

A:

Q: By using an appropriate transformation, evaluate the integral y2\ 1/2 dædy .2 I R. 36 4 when R is…

A: We have to evaluate the given integral.

Q: Use the given transformation to evaluate the integral. 8x2 dA, where R is the region bounded by the…

A:

Q: Use the given transformation to evaluate the integral. lr a?dA, where R is the region bounded by the…

A: Given,

Q: Evaluate the double integral f(r, 0) dA. -z/2 7 cos(@) r dr de

A: The objective is to evaluate the given double integral

Q: Verify Green's Theorem by evaluating both integrals aM | y? dx + x² dy = dA ax for the given path.…

A:

Q: Use the transformation x = 4u and y = 2v to evaluate the integral ∯R y^2 dA where R is the region…

A:

Q: Use the given transformation to evaluate the integral. 10xy dA, where R is the region in the first…

A: Consider a given region R bounded by the lines y=12x and y=32x,  and the hyperbolas xy=12 and xy=32.…