# Thread: A few integrals..

1. ## A few integrals..

2. Originally Posted by Bracketology
This looks like it is for some kind of online homework...

3. Yea...2 questions out of the 50 I have to do, Can you give me a place to start?

4. Originally Posted by Bracketology
Yea...2 questions out of the 50 I have to do, Can you give me a place to start?
Sure, the area, $\displaystyle A$ between two curves $\displaystyle f(x)$ and $\displaystyle g(x)$ on an interval $[a,b]$ is given by $\displaystyle A = \int_a^b [f(x) - g(x)]~dx$

provided $\displaystyle f(x)$ is always the top function on the interval $\displaystyle [a,b]$

5. Originally Posted by Bracketology
Yea...2 questions out of the 50 I have to do, Can you give me a place to start?
You can use symmetry here and Jhevon's hint then

$\displaystyle \int_0^a (c^2-x^2)-(x^2-c^2) ~dx = 65$

where 'a' is the solution to $\displaystyle c^2-x^2=x^2-c^2\implies x = \frac{c}{\sqrt{2}}$

6. Thanks. I really appreciate it. I worked on this problem a good 20 minutes. and Somehow the c's kept canelling out.

7. Originally Posted by Bracketology
Thanks. I really appreciate it. I worked on this problem a good 20 minutes. and Somehow the c's kept canelling out.
How do the c's cancel out?