- #1
DryRun
Gold Member
- 838
- 4
Homework Statement
http://s2.ipicture.ru/uploads/20120204/iuPLuS1l.png
The attempt at a solution
[itex]x=t^2-1[/itex] and [itex]y=t^2+1[/itex]
[itex]\frac{dx}{dt}=2t[/itex] and [itex]\frac{dy}{dt}=2t[/itex]
The line integral is of the form: [itex]\int P\,.dx+Q\,.dy[/itex]
So, i use direct substitution:
[tex]\int^1_0 4t^3-2t\sin(t^2-1)+2t\cos(t^2+1)\,.dt[/tex]
Is my method correct? I can't integrate any further, as i tried integration by parts for [itex]t\sin(t^2-1)[/itex]and got stuck.
http://s2.ipicture.ru/uploads/20120204/iuPLuS1l.png
The attempt at a solution
[itex]x=t^2-1[/itex] and [itex]y=t^2+1[/itex]
[itex]\frac{dx}{dt}=2t[/itex] and [itex]\frac{dy}{dt}=2t[/itex]
The line integral is of the form: [itex]\int P\,.dx+Q\,.dy[/itex]
So, i use direct substitution:
[tex]\int^1_0 4t^3-2t\sin(t^2-1)+2t\cos(t^2+1)\,.dt[/tex]
Is my method correct? I can't integrate any further, as i tried integration by parts for [itex]t\sin(t^2-1)[/itex]and got stuck.