Find the work done by the force field f in moving an object from a to b. f(x, y) = 6y3/2 i + 9x y j a(1, 1), b(4, 9)

By direct calculation, we will see that the work is equal to 2786.4 J.

Remember that work is equal to force times displacement, then we have that:

Obviously, the path that we take from a to b matters here, so we assume that we take the simplest path, which is a line segment:

Now we just perform the integration, instead of x and y we use:

x = 1 + 3*t

y = 1 + 8*t

And the integral is performed between 0 and 1.

We perform the dot product between the field with the vector b - a = (3, 8), this also makes the end result a scalar.

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