Thread: Integrating with respect to x and y

I am trying to integrate the following shaded area:


I am supposed to solve the problem two ways (by integrating with respect to both x and y). I was having trouble with this one, especially with integrating with respect to y. The integrals that I ended up with when integrating with respect to x are:

Integral from 0 to 2 of 6 - 3x + Integral from 0 to 2 of pi.

Can anyone help out with this? Sorry, I don't know how to use the math tags.

Originally Posted by statelyplump

I am trying to integrate the following shaded area:


I am supposed to solve the problem two ways (by integrating with respect to both x and y). I was having trouble with this one, especially with integrating with respect to y. The integrals that I ended up with when integrating with respect to x are:

Integral from 0 to 2 of 6 - 3x + Integral from 0 to 2 of pi.

Can anyone help out with this? Sorry, I don't know how to use the math tags.

I don't see why you would need a pi in the equation since you're not doing a circle.
Perhaps you can integrate by parts, your first integration limits for your x is 0 to 2, y limits: 3x to 6, your second integration limit would probably be; x limit: 0 to 2, y limit: 6 to (the top curve equation)... But i don't see why you can't just integrate the whole thing in on equation.. x limit: 0 to 2, y limit: 3x to (curve equation).... If I'm wrong somebody please correct me...

For the int. with respect to x, I split it so that it is the top part is a quarter of a circle and then add that to the bottom part. I guess it isn't needed, so I have no idea why I did it!