|Evaluate the line integral: f.(r² + y) dx + (4x – cos(y)) dy where C is the boundary of the square R with vertices (0,0), (5,0), (5, 5) and (0, 5) that has the rectangle with vertices (1, 1), (3, 1), (3, 2) and (1, 2) chopped out of it. (C has two pieces. ) Answer: 69 _X

Q: Evaluate the double integral. I| 2y2 dA, D is the triangular region with vertices (0, 1), (1, 2),…

A:

Q: Evaluate the line integral I of the one-form w = (y+ z) dx + (x + z) dy + 10z dz over the line…

A: We have to find the line integral.

Q: Use the transformation u = 3x + y, v =x+ 2y to evaluate the given integral for the region R bounded…

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 4…

A:

Q: c) Use Green's theorem to evaluate the line integral . x2y2 dx + 4x dy, where C is the boundary of…

A:

Q: Calculate the double integral || x + y)?e -r dx dy where R is the square with vertices (4, 0), (0,…

A: Given: ∫∫Rx+y2ex2-y2 dx dy where R is the square with vertices 4,0, 0,4, -4,0, 0,-4

Q: Evaluate the triple integral of the function f (x, y, 2) = 5r-3y over the solid tetrahedron pounded…

A: we can find outer bounds of XY plane by putting z=0.

Q: Use Green's Theorem to evaluate the line integral. | (x - 4y) dx + (x + y) dy C: boundary of the…

A: The given integral is ∫Cx-4y dx+ x+y dy,  where C is the region bounded by x2+y2=1 and  x2+y2=16 To…

Q: c) Use Green's theorem to evaluate the line integral x2y2 dx + 4x dy, where C is the boundary of the…

A:

Q: Calculate the double integral || (x + y)?ex -ý dx dy where R is the square with vertices (2, 0), (0,…

A:

Q: Evaluate the triple integral ∫∫∫T (x^2) dV where T is the tetrahedron with vertices (0, 0, 0), (1,…

A:

Q: Calculate the Line Integral for the F(x,y) = 6 – 3x – 2y where the boundary curve is C: x^2+4y^2=9

A: F(x,y) = 6 – 3x – 2y  To Find: Calculate the Line Integral for the F(x,y) where the boundary curve…

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

A:

Q: (i) Evaluate the double integral (x + y) dxdy where D is the triangular region in the xy plane with…

A:

Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

A:

Q: Evaluate the double integral [[R E¬Y°DA where R is the triangular region in R² with vertices (0,0),…

A: – “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 6- Evaluate the line integral ScF · dr, where F = [xy, yz, xz] and C is the boundary of the…

A:

Q: Q1 Verify that [Oy²-2x )dx +(2xy +x² xdy = [[ ƏP dA where C is the boundary of a region R R defined…

A: We have to verify ∫Cy2−2xdx+2xy+x2dy=∬R∂Q∂x−∂P∂ydA, where C is the boundary of a region R defined by…

Q: Use Green's Theorem to evaluate the integral In(x2 + 1)dx – xdy, C is the boundary of the region…

A:

Q: Evaluate the triple integral. II (x - y) dV, where E is enclosed by the surfaces z = x2 - 1, z = 1 -…

A: Calculate the points of intersection of the curves, x2-1=1-x22x2=2x2=1x=-1,1 According to the…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. xe-4*…

A:

Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

Q: Use the transformation u = 3x + 2y, v =x+ 3y to evaluate the given integral for the region R bounded…

A:

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

A:

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

A: We are given the following transformation: u=4x+3y, v=x+3y    ⇒    x=u-v3    and…

Q: Use Green's Theorem to evaluate the line integral.       Cy dx + 7x dy C: square with vertices (0,…

A:

Q: |Evaluate the line integral: f.(r² + y) dx + (4x – cos(y)) dy where C is the boundary of the square…

A: According to Greens theorem, the line integral ∮CPdx+Qdy=∬DQx-PydA. BY the extended version of…

Q: Evaluate the line integral F(x, y, z) = (x,-z, y). Jo F. dr where C is given by r(t) = (2t, 3t,…

A: We will use concept of parameterization to solve this.

Q: Dy evaluating both integrals Ne ду dA y² dx + x² dy Əx for the given path. C: rectangle with…

A: We will verify Greens theorem.

Q: 6- Evaluate the line integral fF dr, where F = [xy, yz, xz] and C is the boundary of the hemisphere…

A: the line integral f F dr, where F = [ry, yz, xz] and C is the boundary of the hemisphere x² + y² +…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3…

A:

Q: 4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y…

A:

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: 21 Verify that (y² – 2x )dx +(2xy +x²)dy = || dA where C is the boundary of a region ôy -. R R…

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 6…

A:

Q: Verify that | (y -2x)dx + (2.xy + x² = [] dA where C is the boundary of a region R ây C R defined by…

A:

Q: 14. Find the line integral of f(x, y, z) = V3/(x² + y² + z?) over the curve r(t) = ti + tj + tk, 1 <…

A:

Q: e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? +…

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 2…

A: Given problem:-

Q: Verify Green's theorem in the plane for S(3x² -8y )dx +(4y-6xy)dy, Where C is the boundary of the…

A:

Q: Using Green's theorem, convert the line integral §(6y² dx + 2xdy) to a double integral, where C is…

A: Given integral, ∮C6y2dx+2xdy Here C is the boundary of the square with vertices ±2,2 and ±2,-2.…

Q: Q#03(a): Use Green's theorem to evaluate the line integral f. (x – 3y) dx (4x + y) dy, where C is…

A: Green's theorem

Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

A:

Q: 5) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C…

A:

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: Calculate the double integral || (x + y)?e* - Ý dx dy where R is the square with vertices (2, 0),…

A: According to the given information, it is required to find the integral over R where R is square.

Q: 9. Calculate the triple integral of the function f (x, y, z) = e-(æ²+y²)(1–æ²–y²) over the region B…

A: