How to Find the Area Between Two Curves with No Given Boundaries?

[suspenc3]

Hi, I am having a little trouble with this one, how do you do them when no boundaries are given?

$$y=sin \frac{\pi x}{2}$$

and

$$y=x$$

how do i find the boundaries?

 

[suspenc3]

EDIT:i know how to get the boundaries, but how do i know what numbers to integrate between?

 

[arildno]

Eeh, what about the interval $0\leq{x}\leq{1}$??

 

[suspenc3]

why between 0 and 1
?..also..what is the integral of sin2x?

 

[suspenc3]

In an example in the book they find the points of intersection, is this how i do it?if so how would i find the points of intersection?

 

[arildno]

What does the term "point of intersection" MEAN?
Answer that, and you automatically may set up an equation whose solutions are the points of intersection.

 

[arunbg]

You may graph the function for clearer understanding .

 

[suspenc3]

k..well cancel everyhting i said before..we have the two equations..I want to isolate x..and then find where the two curves intersect...

making it $$\frac{2y}{sin \pi} = x$$ is wrong isn't it?

how do i isolate x?

If I can find the points where the two curves intersect, then I can integrate between these two points to find the Area

 

[arunbg]

Yes, that is wrong.
You have two equations in y and x .
The point of intersection has to satisfy both the conditions .
Now can you form the equation ?

Hint : Try to get an equation in x alone .