- #1
thename1000
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Studying for a test and I can't really grasp a full example problem. I would also like help on a couple further example problems that are not done for me.
Find the exact coordinates of the centriod:
a. y=4-x^2, y=0
b. 3x+2y=6, y=0, x=0
c. y=e^x, y=0, x=0, x=1
d. y=1/x, y=0, x=1, x=2
equation 1: xbar=(1/A) of integral from a to b of xf(x) dx
equation 2: ybar=(1/A) of integral from a to b of (1/2)* [f(x)]^2 dx
A= area
f(x)=the function
a.) I have this entire problem worked out for me. I understand why xbar=0, but not how to solve for ybar. In my notes it goes from the line ybar=equation 2 (with f(x) filled in)
to A= integral of -2 to 2 of (4-x^2)dx
to 2 * integral from 0 to 2 of (4-x^2)dx
I don't know why the limits changed or where the 2 came from.
b-d
Could someone run down how to do these. Don't complete the problem or anything but I'm not sure about:
*What to do with the second conditions. (y=1, x=0, y=0 etc.
*To find x intercepts for integration do I just solve for x?
It looks to me like you follow these steps:
1. Find out if either xbar or ybar are zero (odd). Which saves time.
2. Find area by integrating the function. <<Not clear to me how exactly to do this.
3. Plug A into given equation
4. Integrate
thanks
Homework Statement
Find the exact coordinates of the centriod:
a. y=4-x^2, y=0
b. 3x+2y=6, y=0, x=0
c. y=e^x, y=0, x=0, x=1
d. y=1/x, y=0, x=1, x=2
Homework Equations
equation 1: xbar=(1/A) of integral from a to b of xf(x) dx
equation 2: ybar=(1/A) of integral from a to b of (1/2)* [f(x)]^2 dx
A= area
f(x)=the function
The Attempt at a Solution
a.) I have this entire problem worked out for me. I understand why xbar=0, but not how to solve for ybar. In my notes it goes from the line ybar=equation 2 (with f(x) filled in)
to A= integral of -2 to 2 of (4-x^2)dx
to 2 * integral from 0 to 2 of (4-x^2)dx
I don't know why the limits changed or where the 2 came from.
b-d
Could someone run down how to do these. Don't complete the problem or anything but I'm not sure about:
*What to do with the second conditions. (y=1, x=0, y=0 etc.
*To find x intercepts for integration do I just solve for x?
It looks to me like you follow these steps:
1. Find out if either xbar or ybar are zero (odd). Which saves time.
2. Find area by integrating the function. <<Not clear to me how exactly to do this.
3. Plug A into given equation
4. Integrate
Homework Statement
thanks