
Integral Area
Hello fellow math members!
I can't find this area of this two function intersecion:
Y1=$\displaystyle x^3x$
Y2=sin(pi*x)
For $\displaystyle 1\leq x\leq 1$
From what I know, I need to do y1=y2 initially, right?
But even that I did't get to resolve =/
Any help? ^^
Here is the answer:
Thanks!

Re: Integral Area
A graphical representation of the intersections of the two functions would be sufficient in my opinion, but if you want to be slightly more rigorous:
When x = 1, 0, 1 then both $\displaystyle x^3x = x(x1)(x+1)$ and $\displaystyle sin([pi x)$ = 0
In the interval (1,0), $\displaystyle sin([pi x) > 0$ and $\displaystyle x^3x < 0$ so the two functions cannot be equal.
In the interval (0,1), "" < 0 and "" > 0 so the two functions cannot be equal.
Hence the only intersection points are 1, 0, 1. then set up your integrals.
one will be from 1 to 0 with $\displaystyle sin(pi x)  (x^3x)$ and the other will be from 0 to 1 with $\displaystyle (x^3x)  sin(pi x)$. After solving both, add them to get your total area.

Re: Integral Area
Thanks a lot mate! ;)
Just did it!