Question

) If F ~ = (3x2y-y2)ˆi + (2y - 4x)ˆj, evaluate $\int$ Fd~r along the curve C in the xy plane whose parametric representation is x = t and y = t3

from the point (1, 1) to (2, 8)

Answer 1

Gives

$W=\smallint F.dr$

$F=3(x^2y-y^2)\hat{i}+(2y-4x)\hat{j}$

$$W=(3(x^2y-y^2)\hat{i}+(2y-4x)\hat{j}).(dx\hat{i}+dy \hat{j})$$

$W=(x^3y-y^2x)+(y^2-4xy)$

Poin(1,1) (2,8)

$$W=(2^3\times8-8^2\times2)-(1^3\times1-1^2\times1)+(8^2-4\times2\\\times 8)-(1^2-4\times1\times1)$$

$$W=(2^3\times8-1^2\times1)+(8^2-4\times1\times1)+(8^2-4\times2\times8-4\times1\times1)$$

W=63+60+64-64-4=119N