Use Green's theorem to find the area integral if V(x.y) = (x²+y®)į+ (x²=y®\j¸ where C is a solid region bounded by (-1,0), (1,0) and the parabola y = 2–x² and anticlockwise orientation. Note: Solve the problem using rectangular coordinates. 1. 1 1.7 1.4 1.5 1.4 1.3 1.과 1.1 08 04 04 02 04 06

Q: Exal Express the integral I| 2x²ydA 3x²and as an iterated integral, where R is the region bounded by…

A:

Q: 1. Use Green's Theorem to evaluate the line integral (y + lnx) dx - x²dy over the rectangle in the…

A: (.)  Given line integral is ,             ∮c(y+lnx)dx-x2dy where  c is the rectangle in xy plane…

Q: Region B: Computing the integral of the function f (x, y) = (x + y) cos (x + y), with a triangle…

A: Two point form of the equation x1,y1 and(x2,y2) is  y-y1=y2-y1x2-x1(x-x1)

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

A:

Q: Evaluate the integral (show all work for any partial credit): ez-2 = f (7G-2+-1+ sin(z² – 2) ) dz c…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A:

Q: Find the area bounded by the curves x² + y? – 2x – 24 = 0 y2 – 8x + 16 = 0

A: The area between two curves y1 and y2 such that y2>y1 between the limits x=a to x=b is given by;…

Q: Set up the double integral in rectangular coordinates to compute the area of the surface z = x2 +…

A:

Q: Use Greens Theorem to evalua te the line integral Sr -93 dx +x*dy. where C is the positively onented…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: Cyclic integrals of the form Mdx + Ndy can be calculated using the Green s theorem.

Q: $(8y + x -x)dx + (y + 7x)dy = C (Type an exact answer, using as needed.)

A: Green's Theorem:∮Mdx+Ndy=∬∂N∂x-∂M∂ydx dy

Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

A:

Q: Evaluate the integral by making an appropriate change of variables. dA where R is the trapezoidal…

A:

Q: Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. dy…

A:

Q: Find the indefinite integral. p. xV144x-49 1. -arc sec 7. (17x) +C 12 A) 7x B) 7arc sec +C 12 144x 1…

A: To evaluate the given indefinite integral.

Q: Evaluate the integral ² I = (4+ 6y-y²) dy.

A: I=∫034+6y-y2dy

Q: 2. Rewrite the iterated integral f(a, y, 2)dz dy dz in the order of -√1-z Jo (a) dz dy dr; (b) dr dz…

A: The given integral is, ∫01∫-1-x0∫0y2f(x,y,z)dzdydx. we have to write the iterated integral in the…

Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: Q.2: Let C be the line joining A(-1,0), B(0,1), D(1,1), and E(2,0). Evaluate: Scy dz tor and radius…

A:

Q: Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is…

A: According to the given information, it is required to find the value of integral using Green’s…

Q: Evaluate the triple integral. [[[ 8x² dV, where T is the solid tetrahedron with verticies (0, 0, 0),…

A: Given that: The integral is ∫∫∫T8x2dv. The vertices are (0,0,0),(1,0,0),(0,1,0),(0,0,1). The…

Q: Use two -point gaussian square to approximate the following double integral:

A:

Q: 4+ g(x) = x + 2 1 2 3.

A:

Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…