## anonymous one year ago FInd the area of region enclosed by the given curves y=x+5 y^2=x y=2 y=-1 what I did was sliced it to parts. from o to -1 and 0 to 2 did I do it right? top half delta y and bottom delta x

1. freckles

hello are you here? I would start off with a drawing first

2. freckles

$\int\limits_{-1}^{2} (\text{ \right }-\text{ \left } )dy$

3. anonymous

yes I understand that and I wanted to split it in half at y=0 and take areas separately would that work? @freckles

4. freckles

yes but why do that?

5. freckles

seems much easier just to do one integral $\int\limits_{-1}^2 (y^2-(y-5)) dy$

6. anonymous

I guess I am just over thinking it. because today my teacher was talking about splitting integrals too for some equations

7. freckles

well you have a x=y^2 is right of x=y-5 so x=y^2 is greater than x=y-5

8. freckles

|dw:1442380700153:dw|

9. freckles

it is clear from the picture between y=-1 and y=2 we have x=y^2 is greater than x=y-5 you only need one integral

10. freckles

if the functions had crossed passed and therefore you had some kind of switching of which was greater than you may need more than one integral

11. freckles

for example if you had: |dw:1442380823519:dw| you would need two integrals here

12. freckles

|dw:1442380886729:dw| $\int\limits_{-1}^c (g(y)-f(y))dy+\int\limits_c^2 (f(y)-g(y))$

13. anonymous

ahhhhhhhh I see and yeeah that looks like two different areas for the second example lol thank you!!

14. freckles

oops forgot to write a dy at the end of that one integral

15. freckles

$\int\limits\limits_{-1}^c (g(y)-f(y))dy+\int\limits\limits_c^2 (f(y)-g(y)) \color{red}{ dy}$