The work done by F(x, y) =6 x i + 6xy j along the curve x = y² from (0, 0) to (1, 1) is A) 4.5 B) 9 C) 6 D) 12 E) 0

Question

Quizplus · Accepted Answer

The work done by a vector field along a curve is the line integral of the field along the path. For the given vector field F(x, y) = 6x i + 6xy j and the curve x = y^2, the line integral from (0, 0) to (1, 1) is ∫(0 to 1) [6(y^2) + 6(y^2)y] dy = ∫(0 to 1) [6y^2 + 6y^3] dy = [2y^3 + (3/2)y^4] from 0 to 1 = 2(1)^3 + (3/2)(1)^4 = 2 + 1.5 = 3.5.

The Work Done by F(x, Y) =6 X I