Moments, finding coordinates of the centroid of an area

• Sep 11th 2012, 02:38 PM
CoffeeBird
Moments, finding coordinates of the centroid of an area
I don't know what I'm doing wrong; I'm doing everything the book tells me I need to do-and i've looked at their examples but I keep getting an answer similar but not quite what is in the back of the book. Here are the answers in the back for this problem: (-4/5, -32/7) and I got (-8/5, -96/7)

Anyone see what I'm missing here? Or can anyone show me how you would approach this problem (with only the given curves for information)

Find the coordinates of the centroid of the area bounded by the given curves y=x³ , y=-8 , x=0

M= ∫(upper limit 0 and lower limit -2) x³ dx = ¼x^4 (from 0 to -2) = -4

My= ∫(ul 0 and ll -2) x·x³ dx = 1/5 x^5 (from 0 to -2) = 0-(-32/5) = 32/5

Mx= ∫(ul 0 and ll -8) y·[y^(1/3)] dy= 3/7 [y^(7/3)] (from 0 to -8) = 0-(384/7)= 384/7

M·y̅= Mx, so

-4·y̅= 384/7, y̅= -96/7

M·x̅=My, so

-4·x̅= 32/5, x̅=-8/5
• Sep 11th 2012, 02:52 PM
HallsofIvy
Re: Moments, finding coordinates of the centroid of an area
Quote:

Originally Posted by CoffeeBird
I don't know what I'm doing wrong; I'm doing everything the book tells me I need to do-and i've looked at their examples but I keep getting an answer similar but not quite what is in the back of the book. Here are the answers in the back for this problem: (-4/5, -32/7) and I got (-8/5, -96/7)

Anyone see what I'm missing here?

Find the coordinates of the centroid of the area bounded by the given curves y=x³ , y=-8 , x=0

M= ∫(upper limit 0 and lower limit -2) x³ dx = ¼x^4 (from 0 to -2) = -4

This is NOT the region between y= -8 and \$\displaystyle y= x^3\$, it is the region between y= 0 and \$\displaystyle y= x^3\$.

Quote:

My= ∫(ul 0 and ll -2) x·x³ dx = 1/5 x^5 (from 0 to -2) = 0-(-32/5) = 32/5

Mx= ∫(ul 0 and ll -8) y·[y^(1/3)] dy= 3/7 [y^(7/3)] (from 0 to -8) = 0-(384/7)= 384/7

M·y̅= Mx, so

-4·y̅= 384/7, y̅= -96/7

M·x̅=My, so

-4·x̅= 32/5, x̅=-8/5
• Sep 11th 2012, 03:00 PM
CoffeeBird
Re: Moments, finding coordinates of the centroid of an area
you mean the limits of integration are incorrectly chosen? can you help me figure out what they should be?
• Sep 12th 2012, 11:03 AM
CoffeeBird
Re: Moments, finding coordinates of the centroid of an area
ok i see what happened.