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.