Evaluate the line integral
ydx+x2dy
where C=C1+C2.
C1 is the path of the straight line segment from the origin, (0,0) to the point (4,8).
C2 is the path of the parabola y=−x2+5x+4 from the point (4,8) to the point (7,−10) .

Question

Evaluate the line integral
ydx+x2dy 
where C=C1+C2.
C1 is the path of the straight line segment from the origin, (0,0) to the point (4,8).
C2 is the path of the parabola y=−x2+5x+4 from the point (4,8) to the point (7,−10) .

anonymous · Answer

parameterize for both the paths

anonymous · Answer

??

anonymous · Answer

so for c1 its x=4t y=8t and dx=4 dy=8?

turingtest · Answer

yes

anonymous · Answer

dx=4dt,   dy=8dt

anonymous · Answer

would the bounds from c2 be  $$\int\limits_{8}^{-10}$$ or $$\int\limits_{-10}^{8}$$

anonymous · Answer

top one

anonymous · Answer

i got -2940.667 as the final answer

anonymous · Answer

but im wrong.

turingtest · Answer

I don't understand why the bounds on c2 are 8 to -10 and not 4 to 7

anonymous · Answer

so i should use the x instead of y? the example in my book uses y so i chose that.

turingtest · Answer

each case is different, but here it seems that you would want to parameterize c2 as y(x) -> y(t)=y(x(t)) and x(t)=t

anonymous · Answer

i have that the bounds just always confuse me... so it should be $$\int\limits_{4}^{7} -2t^3 + 4t^2 + 5t + 4$$ ?

anonymous · Answer

with  the dts of course

turingtest · Answer

yeah, that's what I get

anonymous · Answer

i get -534... but its wrong.

turingtest · Answer

I got a slightly different answer
what did you get for the c1 integral?

anonymous · Answer

176/3

anonymous · Answer

c2 -592.66667

turingtest · Answer

I was too afraid of an algebra error to do the c2 evaluation, so.... http://www.wolframalpha.com/input/?i=integral%20from%20t%3D4%20to%20t%3D7%20of%20-2t%5E3%2B4t%5E2%2B5t%2B4dt&t=crmtb01 you can see you likely made some small mistake

turingtest · Answer

I agree with your c1

anonymous · Answer

omg i didnt know you could do that!

turingtest · Answer

uh-oh, don't get into cheating all the time :P
your skills will turn to mush, I just do it to evade algebra stuff like this evaluation

anonymous · Answer

thank you so much! i missed a couple classes on changing coordinates and this and the book wasnt helping me! but now im starting to get it!

turingtest · Answer

happy to help, here's a good source imo: http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsIntro.aspx do we know if we got the last one right yet?

anonymous · Answer

yep! so far they are all correct!

turingtest · Answer

awesome :D

anonymous · Answer

thanks. :)

anonymous · Answer

@ganeshie8