(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate this line integral ∫F. dr, whereF= (3x^{2}sin y)i+ (x^{3}cos y)jbetween the origin (0,0) and the point (2,4):

(a) along straight line y = 2x

(b) along curve y = x^{2}

2. Relevant equations

3. The attempt at a solution

Part (a)

dr= dxi+ dyj

∫ [ (3x^{2}sin y)i+ (x^{3}cos y)j] . [dxi+ dyj]

= ∫ (3x^{2}sin y)dx + (x^{3}cos y)dy

= ∫ d(x^{3}sin y) from [0,0] to [2,4]

Does this mean that this line integral is independent of the path taken?

(b) If the line integral is independent of path, you should get the same answer..

Does dr= dxi+ dyjstill hold given that it's a curve now? do i have to use the "distance along curve" formula:

dr = √[ 1 + (dy/dx)^{2}] dx

I've looked up RHB textbook it says it's fine to simply use dr= dxi+ dyj...

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# Homework Help: Finding this line integral

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