The work done by along the curve from (0, 0) to (1, 1) is

Name: The work done by along the curve from (0, 0) to (1, 1) is
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Question

The work done by  along the curve  from (0, 0) to (1, 1) is

Quizplus · Accepted Answer

The curve from (0,0) to (1,1) can be parameterized by x=t and y=t, where t goes from 0 to 1. Then, the work done is given by the line integral:

∫(y^2-x) dx + (2xy-y)dy

Evaluating this integral along the parameterization yields:

∫t^2-t dt + (2t^2-t)dt = [t^3/3 - t^2/2 + t^2 - t^2/2] from 0 to 1 = 1/3

Thus, the work done is 11ead0bc_8d92_d300_99a0_9b2a867660b9_TB6988_11.

The Work Done by Along the Curve from (0