David and Sandra plan to evaluate line integral ∫ c F . d r , along a path in the xy -plane from (0, 0) to (1,1). The force field is F ( x , y ) = ( x + 2 y ) i + ( − x + y 2 ) j . David chooses the path that runs along the -axis from (0, 0) to (1, 0) and then runs along the vertical line x = 1 from (1, 0) to the final point (1, 1). Sandra chooses the direct path along the diagonal line y = x from (0, 0) to (1, 1). Whose line integral is larger and by how much?
David and Sandra plan to evaluate line integral ∫ c F . d r , along a path in the xy -plane from (0, 0) to (1,1). The force field is F ( x , y ) = ( x + 2 y ) i + ( − x + y 2 ) j . David chooses the path that runs along the -axis from (0, 0) to (1, 0) and then runs along the vertical line x = 1 from (1, 0) to the final point (1, 1). Sandra chooses the direct path along the diagonal line y = x from (0, 0) to (1, 1). Whose line integral is larger and by how much?
David and Sandra plan to evaluate line integral
∫
c
F
.
d
r
,
along a path in the xy-plane from (0, 0) to (1,1). The force field is
F
(
x
,
y
)
=
(
x
+
2
y
)
i
+
(
−
x
+
y
2
)
j
.
David chooses the path that runs along the -axis from (0, 0) to (1, 0) and then runs along the vertical line x = 1 from (1, 0) to the final point (1, 1). Sandra chooses the direct path along the diagonal line y = x from (0, 0) to (1, 1). Whose line integral is larger and by how much?
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
find the work done by the force field F(x,y) =(2y+x²,x²-2x) acting on an object as it moves along upper half circle from (-2,0) to (2,0)
Find the work done by the force F = xyi + (y-x)j over the straight line from (0,0) to (1, - 3).
The amount of work done is|
(Type an integer or a simplified fraction.)
Find the work done by the force field F in moving an object on the line segment from A to B, where F(x, y) = (2y^(3/2) )i + (3x √y)j, A(1, 1), and B(4, 4).
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01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY