A line integral is an integral of a function defined on a 3D curve in space. The key to obtaining an integral that can actually be evaluated using single-variable techniques was constructing a ...

Evaluate the line integral integral C ( y + e square root x ) d x + ( 2 x + cos ( y 2 ) ) d y where C is the counterclockwise boundary of the region enclosed by y = x 2 and x = y 2 Evaluate the line integral over C, where C is the given curve. integral of xy^4 ds over C is the right half of the circle x^2 + y^2 equals 16 oriented counterclockwise.

Evaluate the line integral integral_C (x^2 + y^2) dx + 2 x y dy, where C is the path of the semicircular arc of the circle x^2 + y^2 = 4 starting at (2, 0) and ending at (-2, 0) going counterclockwise

Evaluate the line integral Integral_{C} (x + xy + y) ds where C is the path of the arc along the circle given by x^2 + y^2 = 9, starting at the point (3,0) going counterclockwise making an inscribed angle of 2pi/3.

Evaluate the line integral integral_C 7 y^2 dx + z^2 dy + (100 - x^2) dz over the quarter of the circle of radius 10 in the xz-plane with center at the origin in the quadrant x greater than or equal to 0, z less than or equal to 0, oriented counterclockwi

Evaluate the line integral, integral over C of xyz^2 dS, where C is the line segment from (-2, 4, 0) to (0, 5, 3). Evaluate the line integral. \int_C \frac{-ydx + xdy}{x^2 + y^2}, segment from (7,0) to (0,7).

Common terms like line integral, parametrization How a coil is related to a line integral Evaluating a line integral Common equations related to line integrals and integrating functions over paths

Evaluate the line integrals Integral_{path} F cdot dl for the following vector fields along the given paths: F(x,y,z) = xz hat{x} -y^2z hat{z} along the straight line from (0,1,0) to (1,2,3). Determine the distance y' to the centroid of the shaded area measured from the x axis.

What is the line integral of B between points i and f in the figure? Assume that I = 2.0A . Provide a curve that has two horizontal tangents at the same x value, but no vertical tangents. What is the line integral of \vec{B} between points i and f in the figure? Assume that I = 1.6 A. Express your answer to two significant figures.

Evaluate the line integral integral_C x ds, where C is the curve x = 2 t, y = t^2, 0 less than or equal to t less than or equal to square root 2. Find the line integral of f(x, y) = ye^{x^2} along the curve r(t) = 5 t i + 12 t j, - 2 less than or equal to t less than or …