Area Bounded..

• Jan 18th 2009, 08:34 AM
TWiX
Area Bounded..
hi ..
How are you every1??
Is it important to sketch graphs in finding area bounded questions ?
I remember in high school .. we just equal the functions by each other..
Then suppose that we got x=-1 , x=0 , x=1 from equaling two functions..
Then, we got any number between 1- and 0 to determine which function is greater in the interval and the same thing to 0 and 1 .. and we use 2 Integrals (two in this case) ..
but now in college we should SKETCH!!

Any help??
• Jan 18th 2009, 08:40 AM
Mush
Quote:

Originally Posted by TWiX
hi ..
How are you every1??
Is it important to sketch graphs in finding area bounded questions ?
I remember in high school .. we just equal the functions by each other..
Then suppose that we got x=-1 , x=0 , x=1 from equaling two functions..
Then, we got any number between 1- and 0 to determine which function is greater in the interval and the same thing to 0 and 1 .. and we use 2 Integrals (two in this case) ..
but now in college we should SKETCH!!

Any help??

It's very important to sketch. The area you are trying to find often results in the interaction between two functions. If you misinterpret how these function interact graphically, then you will get a wrong answer.
• Jan 18th 2009, 08:53 AM
Jester
Quote:

Originally Posted by Mush
It's very important to sketch. The area you are trying to find often results in the interaction between two functions. If you misinterpret how these function interact graphically, then you will get a wrong answer.

I second that. Here's a simple example. Find the area between $\displaystyle y = x\; \text{and}\; y=x^3$. The curves intesect at $\displaystyle x = -1,\, 0\; \text{and}\; 1$. We know the area between cuves can be found using

$\displaystyle \int_a^b f(x) - g(x)\; dx$
So in this case, what's $\displaystyle f(x)\; \text{and}\; g(x)$? A graph easily gives you these. :)
• Jan 18th 2009, 10:07 AM
Krizalid
Quote:

Originally Posted by danny arrigo

I second that. Here's a simple example. Find the area between $\displaystyle y = x\; \text{and}\; y=x^3$.

Examples like this one can be done by not using graphs, but, most of them requires a sketch to do the problem well.
• Jan 18th 2009, 12:09 PM
Jester
Quote:

Originally Posted by Krizalid
Examples like this one can be done by not using graphs, but, most of them requires a sketch to do the problem well.

I believe I used the word simple example. In my experience alot of students cannot produce

$\displaystyle \int_{-1}^0 \left( x^3-x \right)\,dx + \int_0^1 \left( x - x^3 \right)\,dx$

for the correct area.