Answer
$22 J$
Work Step by Step
The work done in moving the object can be calculated as:
$W=\int_c F \cdot T ds \approx \Sigma_{i=1}^{7} [F(x_i,y_i) \cdot (x_i,y_i)]ds]$
or, $W=(2+2+2+2+1+1+1) \cdot 2 \approx 22 J$
Therefore, we estimate the work done is $22 J$.