http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Wed, 30 Jul 2014 07:15:50 -0500http://calc3.askbot.com/question/197/section-163/Number 8 in section 16.3 asks, Evaluate $\int (10x^4=2xy^3)dx-3x^2y^2dy$ where $C$ is the part of the curve $x^5-5x^2y^2-7x^2=0$ from $(0,0)$ to $(3,2)$. Can someone explain how to solve something like this?AnonymousWed, 30 Jul 2014 07:15:50 -0500http://calc3.askbot.com/question/197/http://calc3.askbot.com/question/186/how-do-i-get-the-bounds-of-integration-for-line-integrals/I am currently working on the homework for 16.2. Number one, for example, states: **"Compute $\int\limits_Cxy^2ds$ along the line segment from (1,2,0) to (2,1,3)"**. I am setting it up as follows: For my parameterized line I get: $$\vec{p}(t) = \langle1,2,0\rangle + t\langle1,-1,3\rangle$$ Giving me: $$x=t+1$$ $$ x' = 1$$ $$y=2-t$$ $$ y'= -1$$ $$z=3t$$ $$ z'= 3$$ Then setting up an integral to compute: $$\int(t+1)(2-t)^2\sqrt{(1)^2+(-1)^2+(3)^2}dt$$ What I am not sure of is how to know what my bounds of integration are. Do I plug my point values in for x, y, and z? Or in this case, for x and y and then solve for t? Or just for x? I would love any help on this or to know if what I have done so far is correct or not correct...Thanks! ChristinaMon, 28 Jul 2014 12:06:32 -0500http://calc3.askbot.com/question/186/