Solve the problem, calculate the line integral of f along h

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.

Do the math. she originally had 50 dollars on her gift card and she had 12 dollars left on her gift card after she finished her shopping spree. if you subtract 50 minus 12 you get thirty eight dollars as your answer. so therefore, ciara spent 38 dollars total o