Calculate the work done by the force `vec(F) = y hat(i)` to move the particle from (0,0) to (1,1) in the following condition
(a) y = x (b) y = `x^(2)`

Explanation

We know that
dw = `vec(F).d vec(s) " " rArr " " dw = (y hat(i)) . (dx hat(i))`
dw = ydx ….(1)
In equation (1) we can calculate work done only when we know the path taken by the particle. Either
y = x or y = `x^(2)` so now
(a) when y = x
`int dw = int_(0)^(1) ` xdx `" "rArr " " w = (1)/(2) `Joule
(b) when y = `x^(2)`
`int " dw " = int_(0)^(1) x^(2) "dx " rArr" " w = (1)/(3) `Joule