Line Integrals
asked 2014-07-29 06:58:55 -0600
I'm hoping someone can show me what I am doing wrong with this. In section 16.2, question #3, it asks you to compute $\int (z\cos(xy))ds$ along the line segment from $(1,0,1)$ to $(2,2,3).$ Here is my calculations: $$P(t)=<1,0,1>+<t,2t,2t>$$ $$\int_1^2 (1+2t)\cos(2t+2t^2)\sqrt{1^2+2^2+2^2}dt$$ $$u=2t+2t^2$$ $$\frac{du}{2(1+2t)}=dt$$ $$3\int_1^2 (\cos(u)(1+2t)\frac{1}{2(1+2t)})du$$ $$\frac{3}{2}\int_1^2 (\cos(u))du$$ $$\frac{3}{2}\sin(u)\biggr|_1^2$$ $$\frac{3}{2}\sin(2)-\frac{3}{2}\sin(1)$$ where did I go wrong?
