# Least Area bounded

Area bounded by f(x) = $$x^3/3$$ - $$x^2$$ +a and the straight line x=0, x=2 and the x axis is minimum. Find a

This is the screen shot of the function when a=0.6.

Scrolling the value of "a" from 0 to 9, I am finding the function to have least value between 0.6 to 0.7...How to prove this mathematically?

• Do you have any ideas about how to calculate the area mathematically? – Minus One-Twelfth Feb 15 at 5:00
• Yes. I believe it comes from integration of bounded functions – Scáthach Feb 15 at 5:02
• But with "a"as a parameter, how will it help us? – Scáthach Feb 15 at 5:03
• Correct! We can use integration. Maybe you can try using integration to find the area as a function of $a$, and then investigate this function. – Minus One-Twelfth Feb 15 at 5:04
• Okay. Let me try then – Scáthach Feb 15 at 5:06