Physical Applications of the Definite Inregrals: b^2 x^2 + a^2 y^2 = a^2 b^2

Lynn Jeferson

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Good Day!!! So we are on Physical application of the definite integrals. and We are suppose to Find the Centroid of the area bounded or enclosed by the given curves . We are taught to get the graph ready first before proceeding to integrating.

The problem is that, i dont know how to plot the given problems.

it asks for:, First Quadrant area of (b^2.x^2)+(a^2.y^2)=(a^2.b^2) please help me!\



1st-quadrant area of \(\displaystyle \, b^2\, x^2\, +\, a^2\, y^2\, =\, a^2\, b^2\)
 
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Well, I'm assuming that you've included the full and exact problem text, and you were given no information about the value(s) of a and b, nor how they relate to x and y. That's okay, it just means the centroid will be expressed in terms of a and b instead of just being a number. One way to begin is to assign some values to a and b and see how the graph changes. The trivial case of a = b = 0 results in no graph, but maybe start with a = b = 1. Then fix b at 1 and let a vary. What happens to the graph? Now fix a and let b vary. What happens to the graph?

Now, using what you've learned about the centroid and the various formulae given to you in your book/handouts/class notes, what do you think an appropriate next step would be? Please comply with the Read Before Posting and share with us all of the work you've done on this problem, even the parts you know for sure are wrong. Thank you.
 
Good Day!!! So we are on Physical application of the definite integrals. and We are suppose to Find the Centroid of the area bounded or enclosed by the given curves . We are taught to get the graph ready first before proceeding to integrating.

The problem is that, i dont know how to plot the given problems.

it asks for:, First Quadrant area of (b^2.x^2)+(a^2.y^2)=(a^2.b^2) please help me!

What would be the shape of the area, if you were given first quadrant of:

(x/a)^2 + (y/b)^2 = 1

Does that equation look familiar?
 
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