Understanding Integration: A Simple Explanation

[ozone]

If one could just explain how the attached answer below was derived I would be greatful. Thanks!

 

[sir_manning]

By being very careful with your minus signs! What did you try? Remember that 'a' is a constant and you are integrating with respect to 'x'.

 

[dynamicsolo]

The anti-derivative function is $$a^{2}x - \frac{1}{3} x^{3} .$$ You then evaluate it at x = a and x = -a (or at x = a and double the result, since the integrand function is symmetrical about the y-axis [the anti-derivative is zero at x = 0 ] ).