The equation of a line is given below.
1 answer:
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Answer:
See below
Step-by-step explanation:
First, I would choose three different points with some distance between. Let's do x = -5, x = 0, and x = 5. Next, I would plug those numbers into the equation, like so:
Next, I would plot the points [(-5, 45), (0, 25), (5, 5)] on an x-y graph. Finally, I would take a ruler, line it up with the three points, and draw a line through those three points, extending from one side of the graph to the other to show the equation is continuous.
The curve 
is parameterized by
so in the line integral, we have
You are mistaken in thinking that the gradient theorem applies here. Recall that for a scalar function
, we have gradient 
. The theorem itself then says that the line integral of 
along a curve 
parameterized by 
, where 
, is given by
Specifically, in order for this theorem to even be considered in the first place, we would need to be integrating with respect to a vector field.
But this isn't the case: we're integrating
, a scalar function.
so in the line integral, we have
You are mistaken in thinking that the gradient theorem applies here. Recall that for a scalar function
Specifically, in order for this theorem to even be considered in the first place, we would need to be integrating with respect to a vector field.
But this isn't the case: we're integrating