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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 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).
Evaluate the line integral, where C is the given curve. integral xy^2 ds, C is the right half of the circle x^2 + y^2 = 16 oriented counterclockwise; Evaluate the line integral Integral_C (x^2 + y^2) dx + 2xy dy, where C is the path of the semicircular arc of the circle x^2 + y^2 = 25 starting at (5, 0) and ending at (-5, 0) going counterclockwise.
Evaluate the line integral integral_C 5 y dx + 4 x dy, where C is the straight-line path from (4, 4) to (9, 7). Evaluate the line integral \int_C4 3ydx + 3xdy where C is the straight line path from (0, 1) to (6, 7).
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 (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 2y dx + 3x dy where C is the straight line path from (4, 2) to (8, 7). Evaluate the line integral over C of 6y dx + 4x dy, where C is the straight line path from (3, 2) to (6, 5).
Given that the line integral is independent of path in the entire xy-plane, calculate the value of the line integral: integral_(pi/2, pi/2)^(pi pi) (cos y + y sin x) dx + (cos x + x sin y) dy; Evaluate the line integral \oint y^2 \,dx + 4xy \,dy along the closed path defined by y =x^2 and y = 2x starting from (0,0), going counter clockwise.
Compute the line integral with respect to arc length of the function f(x, y, z) = x y^2 along the parametrized curve that is the line segment from ( 1, 1, 1) to ( 2 , 2 , 2 ) followed by the line segment from (2, 2, 2) to (-3, 6, 9). Evaluate the line integral Integral_{C} x dS for the curve C. When C is a line segment joining (1,1) to (4,5).
Evaluate the line integral, where C is the given curve. integral_C x^2 y square root z dz, C: x = t^3, y = t, z = t^2, 0 less than or equal to t less than or equal to 1. Evaluate the line integral, where C is the given curve. integral_C x^5 y square root z dz, C: x = t^2, y = t, z = t^2, 0 less than or equal to t less than or equal to 1