Q10. Calculate the integral ſ F dr, where F(x, y, z) = (2x²lny) i + ( + z³)j + 2xzk and C is the curve with parameterization r(t) = ti + t²j+ tk with 1 ≤ t ≤ 2e without using the Fundamental theorem of line integrals.

Q: Evaluate the line integral f y(tan x + x sec² x) dx + x tanæ dy + dz once around the circle x² + y²…

A:

Q: Evaluate the line integral feF. dr where F = (4 sin x, -3 cos y, 5xz) and C is the path given by…

A:

Q: 3. Let f(z) = 1-z and y(t) = t+it for t E-1,1). (a) Sketch the image of the curve y. (b) Evaluate…

A:

Q: use the Fundamental Theorem of line Integrals to evaluate F. dR, where F (*.y) = < y. - X and C is…

A:

Q: Use the Fundamental Theorem of Line Integrals to compute the work done F on an object that is moved…

A:

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

A:

Q: Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a…

A:

Q: Evaluate the line integral f, F . dr, where C is the curve given by F(t) = 3 cos ti+ 3 sin t j, 0<t<…

A:

Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: F. dr where F = yzi + xzj +xyk and C is the curve x = t, y = 2t², z = –2t² with 0<t < 1.

A: Given F=yzi+xzj+xyk and r=ti+2t2j-2t2k Now the vector field along the curve can be given by…

Q: | (xy dx + 2y dy)

A:

Q: Sc xe¹zdS, C is the line segment from (0,0,0) to (1, 2, 3)

A:

Q: Previous Problem List Next ‚ Let F = (6x²y + 2y³ + 7e²)i + (5ex² +54x) j. Consider the line integral…

A: Given, and consider the line integral of  around the circle of radius , centered at the origin and…

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