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# Find the work done by the force field $\mathbf{F}(x, y)=x \mathbf{i}+(y+2) \mathbf{j}$ in moving an object along an arch of the cycloid $\mathbf{r}(t)=(t-\sin t) \mathbf{i}+(1-\cos t) \mathbf{j}$ 0$\leqslant t \leqslant 2 \pi$

## Work done $=2 \pi^{2}$

Vector Calculus

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### Video Transcript

The solution to the question. 39 years here work done by a force field F. Along the path. C. Can be calculated by integral over the regency have got the yard. So we are given that artie is equals to t minus sign T. I plus one minus cause T. J. So first we will be differentiating this with respect to T. So your dear will be equal to one minus caused T. High plus sign T. J. And to dating. And here F. F X comma Y is given us X. I plus Y plus two J. So the F. Of our T. Will be equal to t minus sign. T. Hi bless 1- caused T 1- Costea plus two jay. So now uh moving further your F of our T. Can be written as t minus sign T I plus three minus costea jay. Now integration over the regency half of RT Will be called to integration from 0 to 2 pi t minus sign t minus 70 high plus three minus cause T. J. And to 1- was T. I plus scientists. Yeah. DT solving this integral, you will get your answers uh minus Hi Plus two By Square. So as you know that Your eye is zero. So your answer will be to buy square. Thank you.

Vector Calculus

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