Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y) = xy i + 6y2 j r(t) = 14t4 i + t6 j, 0 ≤ t ≤ 1

Applying each separate step, it is found that the result of the line integral along the vector field is given by 58.

The curve is:

The vector field is:

Applying the vector field at the curve, we have that:

The derivative of the vector field is:

The dot product of the vector field along the curve with the derivative is:

Hence, the line integral is:

The result of the line integral is of 58.

A similar problem is given at link

Then the line integral is

step-by-step explanation:

divide, then simplify your answer.

1. make -15.66 ÷   5.8 a fraction. then divide.

2. simplify.  

3. final answer.