The following problem is given:
fa(x)=ax^2
g(x)=x^3
The area enclosed by fa(x) en g(x) has a size of 12.
Calculate a.
Ok, this is in the chapter explaining integrals, so you have an idea what stuff this is.
I can state
(capital F means 'primitive function of f')
Fa(x)=(a/3)x^3
G(x)=(1/4)x^4
So now I get:
Fa(x)-G(x)=12
(a/3)x^3-(1/4)x^4=12
And I've got a system with 2 unknows, which I cannot solve.
Help would be appreciated, exam is tommorow.
EDIT: If I realise that fa=g on the intersection, I can write out ax^2=x^3 so x=a, and I can integrate:
12=(F(a)-F(0))-(G(a)-G(0))
/me is stupid.
Anyway, you guys CAN help me by devising more problems more or less like this one. Try to make them hard, but solvable. If no-one can think of anything, the admins can close this.
