An object has a displacement from position vector vec(r )_(1)= (2hat(i) + 3hat(j))m " to " vec(r )_(2)= (4hat(i) + 6hat(j))m under a force vec(F) = (3x^(2) hat(i) + 2y hat(j))N. Find the work done by this force

An object has a displacement from position vector vec(r )_(1)= (2hat(i

1.	An object has a displacement from position vector vec(r )_(1)= (2hat(i) + 3hat(j))m " to " vec(r )_(2)= (4hat(i) + 6hat(j))m under a force vec(F) = (3x^(2) hat(i) + 2y hat(j))N. Find the work done by this force
Answer» Solution :`W= underse(r_(1))OVERSET(vec(r )_(1))INT vec(F).d vec(r )= underset(vec(r )_(1))overset(vec(r )_(2))int (3x^(2) hat(i) + 2y hat(J)).(DX hat(i) + dy hat(j) + dz hat(k))` `=underset(2)overset(4)int 3x^(2) dx + underset(3)overset^(6)int 2y dy - [x^(3)]_(2)^(4) + [y^(2)]_(3)^(6)= 83J`