
Proper Integration
Hello I am new.
Question:
Find the area bounded by the graph of each of the following functions, the xaxis and the given coordinates. Sketch the graph in case.
f(x)=2xx^2 ; x=0 to x=2.
My attempt:
=2x(x^2/2)(x^3/3)
=(0)  (2(2)  (2)^2/2)  (2)^3/3)
=0 (42(8/3))
=0  (2/3)
Absolute value gives me:
2/3
But the answer is not right it is:
3.
I don't get it please help.
Thank you.


The graph of $\displaystyle y= 2 x x^2$ crosses the xaxis at x= 1. The region bounded by those graphs has a portion above the xaxis and a portion below it. Since area is always positive and integrating a negative function give a negative result the area is
$\displaystyle \int_0^1 (2 x x^2) dx+ \int_1^2 (2 x x^2) dx$