SOLUTION: Find the area enclosed between the curve y = x(x - 1)2 and the axis y = 0, establishing first where they intersect.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the area enclosed between the curve y = x(x - 1)2 and the axis y = 0, establishing first where they intersect.      Log On


   

Question 876816: Find the area enclosed between the curve y = x(x - 1)2 and the axis y = 0,
establishing first where they intersect.
Found 2 solutions by Fombitz, richard1234:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-3%2C3%2C-3%2C3%2Cx%2A%28x-1%29%5E2%29
From the graph, it looks like the limits of integration are x=0 and x=1
int%28%28x%2A%28x-1%29%5E2%29%2Cdx%2C0%2C1%29=int%28%28x%5E3-2x%5E2%2Bx%29%2Cdx%2C0%2C1%29
int%28%28x%2A%28x-1%29%5E2%29%2Cdx%2C0%2C1%29=x%5E4%2F4-%282%2F3%29x%5E3%2Bx%5E2%2F2%2BC
int%28%28x%2A%28x-1%29%5E2%29%2Cdx%2C0%2C1%29=1%2F4-2%2F3%2B1%2F2
int%28%28x%2A%28x-1%29%5E2%29%2Cdx%2C0%2C1%29=1%2F12

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The curve and the line y = 0 intersect at x = 0 and x = 1. Since x(x-1)^2 is positive along (0,1), the area enclosed is