# Area between two curves

#### suspenc3

Hi, im 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?

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#### suspenc3

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

#### arildno

Homework Helper
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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

Homework Helper
Gold Member
Dearly Missed
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 isnt 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 .

"Area between two curves"

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