General

Chat

Need Some Math Help

Find the area of the region between the curve x=y^(2/3) and the curve x=2-y^4 . I'm having trouble setting up my integral since I don't exactly see the region I'm suppose to find when I plot the graphs.

November 10, 2012

7 Comments • Newest first

Mathematician

[quote=Watermelon]When you find the points, for example: -2 , 2

You can choose 1 because it is in between -2 and 2.

f1(1) = 2x + 1 = 2 * 1 + 1 = 3
f2(1) = 3x + 1 = 3 * 1 + 1 = 4

f2 > f1

y2 - y1[/quote]

Thanks, that was the main problem that was bothering me.

Reply November 10, 2012
Watermelon

When you find the points, for example: -2 , 2

You can choose 1 because it is in between -2 and 2.

f1(1) = 2x + 1 = 2 * 1 + 1 = 3
f2(1) = 3x + 1 = 3 * 1 + 1 = 4

f2 > f1

y2 - y1

Reply November 10, 2012 - edited
Mathematician

[quote=LampShadow]Like what watermelon said:

- Set the equations equal to each other, then find the points where they intersect
- Set up the integrals for both equations, subtracting the "lower" equation from the "upper" one. And then use the y points you found before^ as the bounds.
- Solve

That's pretty much it

*edit: if the x and y switch is bothering you, just ignore it. Treat the x variable on the "y axis" and the y variable on the "x axis", then solve it like you would normally. Instead of x boundaries in the integral, use the y points as the bounds[/quote]

How do I know which is the upper and which one is the lower?

Reply November 10, 2012 - edited
LampShadow

Like what watermelon said:

- Set the equations equal to each other, then find the points where they intersect
- Set up the integrals for both equations, subtracting the "lower" equation from the "upper" one. And then use the y points you found before^ as the bounds.
- Solve

That's pretty much it

*edit: if the x and y switch is bothering you, just ignore it. Treat the x variable on the "y axis" and the y variable on the "x axis", then solve it like you would normally. Instead of x boundaries in the integral, use the y points as the bounds

Reply November 10, 2012 - edited
Watermelon

Solve the spots where the curves cut each other and integrate y1 - y2 with those spots.

Reply November 10, 2012 - edited