00:01
In this question, we need to obtain the work done by a force f on a particle moving around a closed work c.
00:10
Now, the force is given by x -rays to part 3 over 2 minus 8y icap plus 5x plus 7 square root of y, j -cap, where c is a triangle having vertices 0 -0 ,000, 05 and 5 .0.
00:36
Now the formula for work done is w is equal to integration over closed 12c f.
00:42
F dot dr.
00:44
Reputing the value of f we get integration over c, x x x x 2 by 2 minus 8y, i cap plus 5x plus 7 square root of y, j cap times d r.
01:04
Multiplying it by d bar, we get x x r s to per 3 by 2 minus 8 y d x plus 5x plus 7 square root of y, d .y.
01:23
Mark this as equation 1.
01:26
Now, according to the green's theorem, the equation for green theorem is given by integration over c, p d x plus q d y is equal to double integration over d curly q over curly x minus curly p over curly y times d a further substituting the values of now comparing the equation one with the left hand side of the green stuhrum we get the value of p s x raised to part three by two minus eight y and q as five x plus seven spin square root of y.
02:15
Now, using the green theorem, the work then is given by double integration over d.
02:23
Curly over curly x of 5x plus 7 square root of y minus curly over curly y of x x x 3x minus 8 y times b a.
02:40
Further, differentiating we get double integration over d, 5 minus negative of 8 d .a...