Thread: Sin X Squared & Center of gravity

Hi, I'm New to this forum so hello everyone!

Ive been asked to find the center of gravity of Sin x squared, between the limits of 0 -180 degrees.

I am a bit lost, once plotted how could i find the center of gravity between 0-180?

Thanks

Could you tell us more about the problem? A function, such as "$\displaystyle sin^2(x)$" or "$\displaystyle sin(x^2)$" does not have a "center of gravity". That requires a physical object. A geometric object may have a "center" or "centroid" which can be calculated in the same way as a center of gravity and so called (but incorrectly in my opinion) "center of gravity". But you don't even have a geometric figure. Do you mean the center of gravity of two dimensional figure with boundary the graph of the given function and the x-axis? Or the center of gravity of the one dimensional curve? Or some other figure?

So please: do you mean the center of
1) The curve $\displaystyle y= sin^2(x)$

2) The curve $\displaystyle y= sin(x^2)$

3) The area between the graph of $\displaystyle y= sin^2(x)$ and the x- axis

4) The area between the graph of $\displaystyle y= sin(x^2)$ and the x- axis

or something else?

thanks for your reply, apologies for not being clearer!

it is the 4th option which I am trying to find and it would be the centroid as you put it.

Thanks.