Question

We're doing a lab in my Calc II class and I'm stuck on this question. I tried to do it by looking at instructions for a similar question in the book, but it made me more confused. Here is the question and my work:

Find the area of the region enclosed by the lines and curves:
x-(y^2)=0 and x+2(y^2)=3

Here is my work:
x= (y^2) and x= 3-2(y^2)
(y^2)= 3-2(y^2)
3(y^2)-3=0
3((y^2)-1)=0
3(y+1)(y-1)=0
y=-1, 1
That's following what the book showed my to do. However, the book used those y values as the upper and lower bounds of the integral, but by looking at the graph that doesn't make any sense. If I used those as the upper and lower bounds, the answer I got was 4 units^2. How do I do this problem?

Answer 1

I still keep getting 4. At this step:
area= int (3-2y^2-y^2) dy
= int (3(y^2-1) dy
shouldn't it be int(3(1-y^2)?
I did this:

3int(dy)-3int(y^2)dy= 3y- (3(y^3)/3) = 3y-(y^3) from 1 to -1... filling those in, I get 4. Am I still making a mistake?