Answer
a) $-81.33 \ J$
b) $ -221.34 \ J$
Work Step by Step
We know that the energy stored is equal to the negative integral of the force with respect to distance. Thus, we find:
a) $U=-\int_0^{7.5} (.43x - .033x^2+.00086x^3)dx$
Evaluating this integral gives:
$U = -8.133 = -81.33 \ J$
b) $U=-\int_0^{15} (.43x - .033x^2+.00086x^3)dx$
Evaluating this integral gives:
$U = -22.134 = -221.34 \ J$
