Question

Evaluate the line integral

C

F · dr,

where C is given by the vector function r(t).

F(x, y) = xy i + 9y² j

r(t) = 16t⁶ i + t⁴ j, 0 ≤ t ≤ 1

Answer 1

we know that,

where t ranges from t = a to t = b

we have,

Hence we can write,

we have,

Hence,

we have,

As given we have,

Hence we can say that t ranges from t = 0 to t = 1

Hence using formula 1) we can say that,