Given the force field f, find the work required to move an object on the given oriented curve.
f = on the path consisting of the line segment from (-1,0) to (0,8) followed by the line segment from (0,8) to (2,8)

67/4

Step-by-step explanation:

Let C, D be the line segments that join (-1,0) with (0,8) and (0,8) with (2,8) respectively.

The work required by the force field F(x,y)=(x,y) is the curve integral

the line segments that joins (-1,0) with (0,8) can be parameterized as

r(t) = t(0,8)+(1-t)(-1,0)=(t-1,8t) with 0≤ t≤ 1

So

the line segments that joins (0,8) with (2,8) can be parameterized as

r(t) = t(2,8)+(1-t)(0,8)=(2t,8) with 0≤ t≤ 1

hence

and we have the work required by F to move a particle alon the path is

step-by-step explanation:

in the absence of parentheses, i will have to make some assumptions:   i interpret your (3x+5/y^6)(4y^3/5)​ to mean:

3x + 5     4y^(3/5)       (3x + 5)(4)

* =

    y^6             1               y^(6-3/5)

if this is not what you expected, repost your question using parentheses to indicate whether you meant

4y^3

    or   4y^(3/5)

    5

answer: 1 + 1 = 11

step-by-step explanation: