Respuesta :

LammettHash
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]

To answer this question we need to apply the concept of work, that is

w = ∫ ₐᵇ F×ds

Solution is:

w = 523 J

w = ∫ₐᵇ F × ds

F = 2y³/² i + 3xy j        and    ds = dx i + dy j

Then  F × ds  = ( 2y³/² i + 3xy j ) × ( dx i + dy j )

F × ds  = 2y³/² dx + 3xy dy

And     = ∫ₐᵇ F×ds   =  ∫ₐᵇ2y³/² dx + 3xy dy       a  ( 1 , 1 )   b ( 3 , 9 )

∫ₐᵇ F×ds   =  2y³/²∫dx   +  3x ∫ydy

∫ₐᵇ F×ds   =  2y³/²x  |₁,₁³,⁹  + 3xy²/2  |₁,₁³,⁹

∫ₐᵇ F×ds   = 2 × (9)³/² × (3) - 2 × (1 ) ³/²× (1) +  3 × (3)× (9)² /2 - 3 × (1)³/²/2

∫ₐᵇ F×ds   =  162 - 2 + 364,5 - 1,5

∫ₐᵇ F×ds   = 160 + 363

∫ₐᵇ F×ds   = 523 J

Related Link : https://brainly.com/question/21588019

Otras preguntas