calculus helppp

Question

Find the area between the curves   f(x)=x²  and ​ g(x) = ax. ​ (Assume a​ > 0)

​(Hint: Your answer will be in terms of​ a.)

The area is

Answer 1

Answer 2

For variable "a" greater than zero, a graphing calculator shows the line of g(x) = ax rising above the

curve of f(x) = x² in Quadrant I with intersections of line and curve at x = 0 and x = a.

Then construct the integral ∫_{(from 0 to a)}[ax − x²]dx which goes to {0.5ax² − x³/3 + C|_{(from 0 to a)}}.

Simplify {0.5ax² − x³/3 + C|_{(from 0 to a)}} to [0.5a(a²) − a³/3 + C] minus [0.5a(0²) − 0³/3 + C] equal

to a³/6.