# Thread: Double (Iterated) Integration. Where am I going wrong?

1. ## Double (Iterated) Integration. Where am I going wrong?

Hello everyone,

I need some help with a simple iterated integration. I just can't seem to figure out where I am going wrong. According to an online homework site, my answer is not correct.

I am getting a crazy answer of -179975.2.

Below is the question and I have attached an image of my work. Any help would be GREATLY appreciated, as this assignment is due soon.

Question:
(1 pt) Let D be the region in the x,y-plane enclosed by the curves and . Find the volume of the solid with base D that lies under the surface .

2. The first thing I can see that is wrong is that your $\displaystyle dx$ and $\displaystyle dy$ are around the wrong way.

That would mean that when you integrate with respect to $\displaystyle y$ first, it should be noted that the $\displaystyle y$ values are bounded by $\displaystyle y = \pm \sqrt{x + 9}$ and $\displaystyle y = \frac{1}{2}x + 3$.

3. Your graph is also wrong. What you have marked as (0, 3) should be (0, -3), because it below the y-axis, and is NOT a point of intersection of the two graphs.

If $\displaystyle x= y^2- 9$ and $\displaystyle x= 2y- 6$ then $\displaystyle x= y^2- 9= 2y- 6$ so that $\displaystyle y^2- 2y- 3= (y+ 1)(y- 3)= 0$. The two graphs intersect where y= -1 and y= 3. When y= -1, x= -8 and when y= 3, x= 0.

The two graphs intersect at (-8, -1) and at (3, 0).

4. Thank you. My D region was incorrect. I only had to change my integration limit from 16 to-9 to 3 to -1 an got the answer correct using the same approach I used.