What is the area of the closed figure formed by the relationship x^2 / 9 + y^2 / 4 = 1?

Isolate y

You get the function y = √(4 - (1/9)x²) = (2² - (x/3)²)^½

When you have a function of the form y = √(r² - x²) the graph with always be a half circle only in the positive range with the radius r.

Therefore you can see, by using a graphics calculator, that your function will draw a half circle with radius 6 but higth of only 2 since x is divided by 3.

Now you must integrate the function with lower limit = -6 and upper limit = 6.

I use the graphics calculator again since I do not know how to do it when x has a coefficient (dividend).

My result is 18.85 ~ 6π.

This is the equation for an ellipse centered at (0,0) with semi-major and minor axes of 3 and 2.

The area for such an ellipse is given by A = pi*a*b = 3.13159*3*2 = 18.85 (or as you say 6pi).

IF you are trying to prove this by integration, you can take just one quadrant and multiply by 4, since it is symmetric about both the x and y axes and the origin.

y = 2sqrt(1 - x^2/9) = 2/3(9 - x^2)^(1/2) integrate from 0 to 3.

This is an ellipse with a=3 and b=2 and center (0,0).

Are you sure the answer is 6PI?

Please consult the reference.

The gist of the controversy accessible (sorry, there are too many pages to furnish each and each of the hyperlinks) is that wands help to concentration the magic resident interior the witch or wizard, yet wandless magic continues to be conceivable, particularly for terribly proficient human beings like Snape and Dumbledore. some examples ... Apparition Assuming one's Animagus style (or Metamorphpagus) Accio (the Summoning appeal) Elves can do magic without utilising wands Lumos

it's not calculus..why integration by parts...center is at (0,0) and r is 2 and 3....2 times 3 times pi