## anonymous 5 years ago how do you find the area enclosed by a line, a parabola, and the x-axis?

1. anonymous

integrate :)

2. anonymous

i know but integrate what

3. myininaya

we need to know what parabola and what line

4. anonymous

if you have x^2 from 0 to 1 its int (0 to 1) of x^2 dx

5. anonymous

as an example

6. anonymous

Find the area enclosed by $y=\sqrt{2x}, y=6-2x, and the xaxis$

7. myininaya

first find where they intersect

8. anonymous

but they intersect at three different places

9. amistre64

those equation only intersect in one place :)

10. anonymous

rearrange for x in the equations, your parabola will then be the lower limit, the straight line will be the upper limit and your y limits will be from 0 to the y component of the intersection point, then it is a trivial double integral

11. myininaya

i will scan and show you my drawing

12. myininaya

13. anonymous

$\int\limits_{0}^{y component of intersection}\int\limits_{(y^2)/2}^{1/2y+3}..and so on$

14. myininaya

i always have to draw picture first

15. anonymous

me too by visual inspection you can simplify the problem a lot

16. myininaya

dana, have you looked at the pic?

17. myininaya

i also put what i integrated

18. myininaya

oops that second integral should e from 2 to 3 i messed up my line a bit

19. anonymous

$\int\limits_{0}^{2}\int\limits_{.5y^2}^{-0.5y-3}dxdy$

20. anonymous

yeaa that makes sence now, thank you!

21. myininaya

there was not suppose to be an e in that sentence lol

22. myininaya

because the x intercept of that y=6-2x is 3 not 4

23. anonymous

yea his way if fine too, the double integral is just another way you can check your answer

24. myininaya

she*

25. myininaya

her*

26. anonymous

oh sorry

27. anonymous

wasn't paying attention to the name there sorry

28. anonymous

but on the other hand that double integral is pretty epic? can someone be my fan i think i deserve it for going all out on this question

29. myininaya

i will be ur fan

30. anonymous

31. anonymous

helped people a few times but it seems a lot of people just make an account to ask a question and then leave without saying thank you

32. myininaya

33. myininaya

he didnt become our fan :(

34. myininaya

dana, if you come back you could have done int(3-y/2-y^2/2,y=0..2) and got the same thing you could have look at the functions as if y-axis was x-axis

35. anonymous

ohh thats true, to switch the problem around. and i did say thank you, for the record. you all were a lot of help! :)

36. myininaya

lol im sorry i didn't notice im an idiot

37. anonymous

are aunder a curve, use integration & subtract lower curve from upper