When finding the area between two curves, to find the bounds can you set the equations equal? The reason I ask is because it seems counter-intuitive but I remember my professor saying you could?

Question

zepdrix · Answer

Yes.
Intersection is where the functions have the same (x,y) coordinate.

So if you're given y=x^2+4 and y=2x+5 for example...
they intersect when they have the same y value,
x^2+4 = y = 2x+5
x^2+4 = 2x+5

From there, you do the algebra to figure out what x coordinate they share.

samigupta8 · Answer

Obviously , we can find the bounds only and only when we equate the equations of 2 curves. The rest is well explained by zep!!

legomyego180 · Answer

Thank you to you both, sorry I didnt respond back sooner, I fell asleep last night.
A follow up question.

I have the problem of finding the area between 

$$f(x)=\left\{ \left(\begin{matrix}5\sqrt{x}, 0\le x \le1 \ 6-x^2, 1< x \le2\end{matrix}\right) \right\}$$

(sorry if this looks weird, it was my best attempt at making a piecewise function)

Would I set

$$5\sqrt{x}=6-x^2$$

to find my bounds here? Or are they already given to me in the domain of the function?

legomyego180 · Answer

@agent0smith

agent0smith · Answer

This is ONE function, not two.

agent0smith · Answer

Just find the area under the given function.

legomyego180 · Answer

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