Do you mean
For ,
Note: for every a>0,
therefore,
so,
Hi, my teacher did the following step, and I cant understand it really:
We have A = b $(With limits from 0 to a) Sqroot [1-x^2 / a^2 ] dx
he got the common denominator as following: a^2 -x^2 / a^2
Now he suddenly wrote it like this ....
b/a $ Sqroot [a^2 - x^2] dx My queston is how did he do this step??
I would have done that slightly differently. Let so that and . When x= 0, so that and when x= a, so that . The integral becomes
.
Or, since this was posted in "Pre-algebra and Algebra", I might recognize that leads to or , an ellipse which has are . Since a square root is always positive, this is the upper portion of that area and has area .