Evaluate the line integral(C) F · dr, where C is given by the vector function r(t).?

Question

F(x, y) = xy i + 9y^2 j
r(t) = 16t^6 i + t^4 j, 0 ≤ t ≤ 1

Answer 1

The function and .

We know that r(t) = x(t) i + y(t) j.

Now comparing these two,

 

Now we solve line integral

 

Therefore .