Find the COG of two cubic curves

[hms.tech]

The first part of the question asks to find the COG of the curve y=[1-x]*x^2 in the interval x=0 to x=1

I found that correctly as (0.6,0.0571)

The next part asks to find the COG of another cubic curve y=x[1-x]^2
But without using integration but by using the result of the first part of the question.

I have absolutely no clue of how to proceed forward.
Please help.
I have tried drawing both curves but it was of no use.

 

[LCKurtz]

The first part of the question asks to find the COG of the curve y=[1-x]*x^2 in the interval x=0 to x=1

I found that correctly as (0.6,0.0571)

The next part asks to find the COG of another cubic curve y=x[1-x]^2
But without using integration but by using the result of the first part of the question.

I have absolutely no clue of how to proceed forward.
Please help.
I have tried drawing both curves but it was of no use.

Look at your graphs again. One of them is the reflection of the other in the line ##x=1/2##. Another thing to notice is if you replace ##x## by ##1-x## in one graph it gives the other. You should be able to use these observations for a shortcut.

 

[Mark44]

What is COG?

 

[LCKurtz]

I assume "center of gravity".

 

[DryRun]

I'm still debating between "Canberra Ornithologists Group" and "Canadian Organic Growers".

 

[hms.tech]

Thanks, I got it...you are a genius (@lckurtz)

 

[hms.tech]

FYI, it is centre of gravity,centre of mass, centroid