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## Homework Statement

Evaluate this line integral ∫

**F**. d

**r**, where

**F**= (3x

^{2}sin y)

**i**+ (x

^{3}cos y)

**j**between the origin (0,0) and the point (2,4):

(a) along straight line y = 2x

(b) along curve y = x

^{2}

## Homework Equations

## The Attempt at a Solution

__Part (a)__d

**r**= dx

**i**+ dy

**j**

∫ [ (3x

^{2}sin y)

**i**+ (x

^{3}cos y)

**j**] . [dx

**i**+ dy

**j**]

= ∫ (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 d

**r**= dx

**i**+ dy

**j**still 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 d

**r**= dx

**i**+ dy

**j**...