# Final in 6 hours! Line Integrals!

• Jul 23rd 2008, 11:55 PM
hottytoddychick
Final in 6 hours! Line Integrals!
My final is in 6 hours. I've been slowly teaching myself line integrals and I'm stumped. Here's the problem:

Integrate f over the given curve:

f (x,y) = x3/y
C: y = x2/2
0<= x <= 2

I don't even know where to start! There's no example like this in the text. I have nothing to follow.

I know I need r(t), |v(t)|, and an interval for t, but I'm completely clueless!

(I know I double posted- could someone please delete the thread in the urgent homework section? Thank you!)
• Jul 24th 2008, 12:23 AM
CaptainBlack
Quote:

Originally Posted by hottytoddychick
My final is in 6 hours. I've been slowly teaching myself line integrals and I'm stumped. Here's the problem:

Integrate f over the given curve:

f (x,y) = x3/y
C: y = x2/2
0<= x <= 2

I don't even know where to start! There's no example like this in the text. I have nothing to follow.

I know I need r(t), |v(t)|, and an interval for t, but I'm completely clueless!

(I know I double posted- could someone please delete the thread in the urgent homework section? Thank you!)

The line element:

ds = (1+|dy/dx| ^2 )^{1/2} dx = (1+x^2)^{1/2} dx

Then:

int_S f(x,y) ds=int_{x=0 to 2} (2x) (1+x^2)^{1/2} dx

RonL
• Jul 24th 2008, 12:36 AM
hottytoddychick
I'm supposed to do a parametrisation to get the integral, and for the answer I got from working out what you gave me, I have (5root5)/10. The answer in the back of the book is (10root5 - 2)/3
• Jul 24th 2008, 03:15 AM
CaptainBlack
Quote:

Originally Posted by hottytoddychick
I'm supposed to do a parametrisation to get the integral, and for the answer I got from working out what you gave me, I have (5root5)/10. The answer in the back of the book is (10root5 - 2)/3

The parameterisation is $t=x$, and check your integration, QuickMath gives the answer from the back of your book.

RonL