Find the area between y = x^3 - 4x^2 and y = x - 4

[TONYYEUNG]

Find the area enclosed between the curves y = x^3 - 4x^2 and y = x - 4.

My solution:

Curves meet when x^3 - 4x^2 = x - 4
So, x^2(x - 4) = x - 4
So, (x^2 - 1)(x - 4) = 0
So, x = ­±1, 4

Could you tell me how can I do for the next steps and get the solution??

 

[tkhunny]

Another negative value? Stop doing that. Area is ALWAYS positive. Integrals don't know how you are using them. You have to know it.

Again, do it in two pieces. [-1,1] and [1,4]

Area is NEVER negative. Don't let it fool you.