In each part, evaluate the integral [tex]\int(3x+2y)dx+(2x-y)dy[/tex]
(A) The line segment from (0,0) to (1,1).
(b) The parabolic arc y=x^2
(c) The curve y=sin(pi(x)/2) from (0,0) to (1,1)
(D) The curve x=y^3 from (0,0) to (1,1).
The Attempt at a Solution
Okay, so I'm not very good with the latex thing, but basically, from my understanding, you just have to parametrize each equation and then integrate from 0 to 1 for all of them right? The book says I should be getting 3 for all parts, but I;m getting things like 4.5 for a and 17/6 for b.
For a, I said that x=t and y=t (I stink at parametrizing, is this right???) which gives an integral of 9t from 0 to 1 which integrates to 4.5.
For b, I said that x=t and y=t^2 (how does one parametrize any given equation? These basic steps have really been killing me, like, how does one figure out the parametric equations for a circle? Everywhere I looked it just looks like it's given. What if i wanted to parametrize an ellipse or something? I think I must have missed a big chunk of my calc sequence or something.) Anyway, i ended up with an integral of 5t+t^2 from 0 to 1, which gives 17/6 if i'm right.
Okay, secondly, I've tried the advanced searches and I swear I can never get the search thing to give me what I want, so I always end wasting 30 minutes writing up the whole question and stuff and then when i post it, it says something like "related posts" at the bottom which are pretty much exactly what would have helped me. I'm so exasperated!! Please help!! help of any kind!!!