  # Previous Problem List Next(1 point)Let F be the radial force field F zi +to (10, 100). (Compare your answers!)Find the work done by this force along the following to curves both which go from (0,0A. If C1 is the parabola:t, y , 0 t10, then F.dr-B. If C2 is the straight line segment:10t2, y-100r2, 0st1, then F.drC2

Question help_outlineImage TranscriptionclosePrevious Problem List Next (1 point) Let F be the radial force field F zi + to (10, 100). (Compare your answers!) Find the work done by this force along the following to curves both which go from (0,0 A. If C1 is the parabola: t, y , 0 t10, then F.dr- B. If C2 is the straight line segment: 10t2, y-100r2, 0st1, then F.dr C2 fullscreen
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Step 1

A.

Given radial force field F = xi + yj

For Parabola C1,   x,y coordinates are x = t , y = t2

Parabola r(t) = t i + t2 j , 0 ≤ t ≤ 10

Apply derivative with respect to t on both sides.

dr(t) = (i + 2tj)dt

F•dr(t)   = (xi + yj).(i + 2tj)dt

= (xi.i + 2tyj.j)dt

since i.i  = j.j = 1

= (x + 2ty)dt

Also, we have x = t , y = t²

F.dr(t) = (t + 2t*t2)dt  =  (t + 2t3)dt

Step 2

Now integrate with respect to t in the interval 0 to 10

Step 3

The work done is...

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### Calculus 