- #1
tomelwood
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Homework Statement
I have to calculate the following line integral
[tex]\int_{\gamma}y^{2}cos(xy^{2})dx + 2xycos(xy^{2})dy[/tex] where [tex]\gamma[/tex] is the path defined by the equations [tex]x(t) = t^{4}[/tex] and [tex] y(t)=sin^{3}(\frac{t\pi}{2})[/tex] t between 0 and 1
Homework Equations
Now I know that the formula for calculating this is the integral over where gamma is defined (ie 0 to 1) of [tex]F(\gamma(t))\bullet\gamma'(t)dt[/tex] where [tex]\bullet [/tex] is the scalar product.
The Attempt at a Solution
Therefore wherever I see an x in the original integral, I can substitute it for [tex]t^{4}[/tex] and similarly for the y subbing with the sin expression. And then instead of dx I put x'(t) and instead of dy I put y'(t) and integrate everything between 0 and 1.
The problem is is that this yields the following horrendous expression, which I don't know how to integrate.
[tex]\int^{1}_{0}(sin^{6}(\frac{t\pi}{2})cos(t^{4}sin^{6}(\frac{t\pi}{2}))4t^{3}+2t^{4}sin^{3}(\frac{t\pi}{2})cos(t^{4}sin^{6}(\frac{t\pi}{2}))\frac{3\pi}{2}sin^{2}(\frac{t\pi}{2})cos(\frac{t\pi}{2})) dt[/tex]
Where have I gone wrong?
Hopefully the Latex works!
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