Evaluate the line integral I of the one-form w = (y + z) dx + (x + 2) dy + 10z dz over the line segment from (0,0,0) to (3, 1, 0). I

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

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

A:

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

A:

Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

A:

Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

Q: Find extrema of f (x, y) = 2x² + 4y² on the unit-circle x + y² = 1.

A: To find the extrema of the function ƒ(x, y) = 2x² + 4y² on the unit-circle x² + y² = 1, we need to…

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

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

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

A:

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

Q: particle started at A(1,0) circled the origin once  an d returned toA(1,0) .what were the change in…

A: Given: A particle started at A(1,0) circled the origin once  and  returns to A(1,0)

Q: Let r (t) = The dot product r (1) · r ' (1) =

A: First differentiate at given value then take dot product

Q: Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x…

A: In the given question we have to find the double integral of paraboloid z=x2-y2 ovet the triangle…

Q: Find the image of the line z =3 +iy under f(z) = e

A: