Find the work done by the force field f in moving an object from a tob. f(x, y) = 2y3/2 i + 3x y j a(1, 1), b(3, 9)

Assuming the path from [tex]a[/tex] to [tex]b[/tex] is a line segment, we can parameterize it by
[tex]\mathbf r(t)=(1-t)(1,1)+t(3,9)=(1+2t,1+8t)=(x(t),y(t))[/tex]
for [tex]0\le t\le1[/tex]. Then the work done by [tex]\mathbf f(x,y)[/tex] along this path, which I'll denote [tex]\mathcal C[/tex], is
[tex]\displaystyle\int_{\mathcal C}\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}f(x(t),y(t))\cdot(2,8)\,\mathrm dt[/tex][tex]=\displaystyle\int_0^1(2(1+8t)^{3/2},3(1+2t)(1+8t))\cdot(2,8)\,\mathrm dt[/tex][tex]=\displaystyle4\int_0^1(1+8t)^{3/2}\,\mathrm dt+24\int_0^1(1+10t+16t^2)\,\mathrm dt[/tex]
[tex]=\dfrac{242}5+272=\dfrac{1602}5[/tex]