# What is the difference between ∫ F∙dr and ∫ ∇f.dr, line integrals problem?

• Jun 12th 2011, 11:39 AM
Walid92
What is the difference between ∫ F∙dr and ∫ ∇f.dr, line integrals problem?
I'm trying to solve this problem

Attachment 21652

and I got the length by substituting dx by dy or the opposite, or I could use the parametric equation.
But the 2nd part is where I stop, please help me I have an exam in few hours :/ can someone explain in details how I would solve part B? Sorry for my english, not my native.
I have an exam tomorrow, please it is urgent.
http://www.mathhelpforum.com/math-he...isc/pencil.png
• Jun 12th 2011, 02:29 PM
mr fantastic
Quote:

Originally Posted by Walid92
I'm trying to solve this problem

Attachment 21652

and I got the length by substituting dx by dy or the opposite, or I could use the parametric equation.
But the 2nd part is where I stop, please help me I have an exam in few hours :/ can someone explain in details how I would solve part B? Sorry for my english, not my native.
I have an exam tomorrow, please it is urgent.
http://www.mathhelpforum.com/math-he...isc/pencil.png

You are expected to know (and it is surely in your class notes and textbook) that $\displaystyle \int \nabla f \cdot dr = f(c, d) - f(a, b)$ where (c, d) are the coordinates of the end of the curve you're integrating along and (a, b) are the coordinates of the start.

And you're expected to know that if $\displaystyle F = \nabla f$ then F is conservative.

These are things you are meant to have learned long before a few hours before an exam on the subject.