Solve the Problem $\mathbf { F }$ Of a Fluid Has a Constant Magnitude

Essay

Solve the problem.
-The velocity field $\mathbf { F }$ of a fluid has a constant magnitude $\mathrm { k }$ and always points towards the origin. Following the smooth curve $y = f ( x )$ from $( a , f ( a ) )$ to $( b , f ( b ) )$ , show that the flow along the curve is
$$\int _ { C } \mathbf { F } \cdot \mathbf { T } d s = k \left[ \left( a ^ { 2 } + ( f ( a ) ) ^ { 2 } \right) ^ { 1 / 2 } - \left( b ^ { 2 } + ( f ( b ) ) ^ { 2 } \right) ^ { 1 / 2 } \right]$$