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 May 21st, 2013, 07:02 PM #1 Senior Member   Joined: Jul 2012 Posts: 225 Thanks: 0 Line integral multivariable calculus simple question Hey, basic question but its new material to me. I'd like to know if i solved correctly, my book doesnt show answers. Calculate the integral: $\int_c xy \mathrm{d}s$ where $c$ is the straight line that connects (2,3) and (-1,1) My answer: $Let x=u, and, y=\frac{2}{3}u+\frac{5}{3}$ $\frac{dx}{du}=1, \frac{dy}{du}=\frac{2}{3}$ $-1\leq u\leq 2$ $J=sqrt{{(\frac{dx}{du})}^{2}+{(\frac{dy}{du})}^{2} }=sqrt{1+\frac{4}{9}}=\frac{sqrt{13}}{3}$ $\int_c xy \mathrm{d}s= \int_{-1}^{2} u(\frac{2}{3}u+\frac{5}{3})*Jdu=\frac{sqrt{13}}{9} \int_{-1}^{2} 2{u}^{2}+5udu=\frac{3sqrt{13}}{2}$ What do you guys think?
 May 22nd, 2013, 06:55 AM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Line integral multivariable calculus simple question I did the problem by taking x= 3t- 1, y= 2t+ 1 and got the same answer. Two great minds can't both be wrong!

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