Question

Find the work done by the force field f in moving an object from a to

Answer 1

Presumably the path from $a$ to $b$ is a line segment, in which case we can parameterize it by

$\mathbf r(t)=(1-t)(1,1)+t(4,9)=(1+3t,1+8t)$

with $0\le t\le1$. Then the work done along this path - denoted by $\mathcal C$ - is

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}(6(1+8t)^{3/2},9(1+3t)(1+8t))\cdot(3,8)\,\mathrm dt$
$=\displaystyle\int_0^1(72(1+3t)(1+8t)+18(1+8t)^{3/2})\,\mathrm dt$
$=\dfrac{6309}5$