- The force exerted by a spring when it’s displaced by x from its
natural length is given by the equation F(x) = −kx, where k is a
positive constant. What is the work done by a spring as it pushes out
from x = −x 2 to x = −x 1 (where x 2 > x 1 )?
Here’s How to Crack It
We sketch the graph of F(x) = −kx and calculate the area under the graph from x =
−x 2 to x = −x 1.
Here, the region is a trapezoid with area A = (base 1 + base 2 ) × height, so