Let f ( x , y )=5 x and let c be the segment of the parabola y = 2 x squared joining o( 0 , 0 ) and p( 1 , 2 ). a. find a parameterization of c in the direction from o to p. evaluate integral from upper c to f ds. b. find a parameterization of c in the direction from p to o. evaluate integral from upper c to f ds.

The parameterization of C in the direction from O to P can be determined by integrating the given function in terms of 't' nad in the same way parameterization of C in the direction from P to O can be determined by integrating the given function in terms of 'w'.

Given :

A) The parameterization of C in the direction from O to P is given by:

where, .

B). The parameterization of C in the direction from P to O is given by:

where, .

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a. We can parameterize by

with . Then

b. We can parameterize the opposite direction by instead setting

with . Then

which gives the same value as in part (a).