To find the work done on the interval from x = -1 to x = 1, we need to calculate the integral of the force function f(x) from -1 to 1:
Work = ∫[from -1 to 1] 1/√(1-x^2) dx
We can rewrite the integral using the substitution method. Let u = 1 - x^2, then du = -2x dx and when x = -1, u = 2, and when x = 1, u = 0. Therefore the integral becomes:
Work = ∫[from 2 to 0] -1/(2√u) du
Work = - ∫[from 2 to 0] 1/(2√u) du
Work = - [1/2 * 2√u] [from 2 to 0]
Work = - [√u] [from 2 to 0]
Work = - [√0 - √2]
Work = - [-√2]
Work = √2
Therefore, the work done on the interval from x = -1 to x = 1 is √2 pounds.
The work done to an object is the product of the force applied and the distance that the object moves: Work = force* distance. The force
used when moving an object on the x-axis from the interval x = - 1 to x = 1 (in feet) is given by f(x) = 1/square root 1-x^2 in pounds. What is the work done on the interval?
1 answer