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I'm used to parameterizing however I'm not sure how to solve these types of problems, any help would be much appreciated.

1) Calculate the line integral ∫

2) a) Find the work that the force

b) Calculate the work done along a straight line from A to C.

c) Since the work done appears to be independent of the path taken, we expect that the force can be written as the gradient to a potential V. Find the potential-function and show that the difference between the potential at A and C are equivalent to the work done.

Attempt at reaching a solution:

1) I substituted y=x

2) Similar thinking to 1) is messing me up I think. Did normal integrals with respect to

1) Calculate the line integral ∫

**v**⋅d**r**along the curve*y*=*x*^{3}in the*xy*-plane when -1≤*x*≤2 and**v**=*xy***i**+*x*^{2}**j**2) a) Find the work that the force

**F**= (*y*^{2}+5)**i**+(2*xy*-8)**j**carries out along two paths ABC and ADC which are composed of perpendicular lines between the points A,B,C,D. A,B,C,D are corners in a square and the corners have the coordinates (0,0),(1,0),(1,1),(0,1) respectivelyb) Calculate the work done along a straight line from A to C.

c) Since the work done appears to be independent of the path taken, we expect that the force can be written as the gradient to a potential V. Find the potential-function and show that the difference between the potential at A and C are equivalent to the work done.

Attempt at reaching a solution:

1) I substituted y=x

^{3}into the equation then did a normal integral with respect to x. It doesn't seem right to me however I'm used to d**S**and*t*so these problems just messed my thinking up.2) Similar thinking to 1) is messing me up I think. Did normal integrals with respect to

*x*and*y.*