line integral

The closed curve shown in the figure is described by r = 1 + cosθ, where r = √x² + y²; x = rcosθ, y = rsinθ The magnitude of the line integral of the vector field F = -yî + xĵ arou...

If f = 2x³ + 3y² + 4z, the value of line integral ∫c gradf ⋅ dr evaluated over contour C formed by the segments (-3, -3, 2)→(2, -3, 2)→(2, 6, 2)→(2, 6, -1) is

Consider the line integral $I = \int_C (x^2 +iy^2)dz$, where $z = x + iy$. The line $C$ is shown in the figure below. The value of $I$ is

As shown in the figure, C is the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of the integral ∫_C (y² + 2yx)dx + (2xy + x²)dy is ________ (up to...

The value of line integral $$\,\,\int {\left( {2x{y^2}dx + 2{x^2}ydy + dz} \right)\,\,} $$ along a path joining the origin $$(0, 0, 0)$$ and the point $$(1, 1, 1)$$ is

The line integral of the vector field $$\,\,F = 5xz\widehat i + \left( {3{x^2} + 2y} \right)\widehat j + {x^2}z\widehat k\,\,$$ along a path from $$(0, 0, 0)$$ to $$(1,1,1)$$ param...

The line integral of function $$F=yzi,$$ in the counterclockwise direction, along the circle $${x^2} + {y^2} = 1$$ at $$z=1$$ is

Given a vector field $$\overrightarrow F = {y^2}x\widehat a{}_x - yz\widehat a{}_y - {x^2}\widehat a{}_z,$$ the line integral $$\int {F.dl} $$ evaluated along a segment on the $$x-...

$$$F\left(x,y\right)=\left(x^2\;+\;xy\right)\;{\widehat a}_x\;+\;\left(y^2\;+\;xy\right)\;{\widehat a}_y$$$. Its line integral over the straight line from (x, y)=(0,2) to (2,0) eva...

$$F\left( {x,y} \right) = \left( {{x^2} + xy} \right)\,\widehat a{}_x + \left( {{y^2} + xy} \right)\,\widehat a{}_y.\,\,$$ Its line integral over the straight line from $$(x, y)=(0...