# Area bounded by...

• Jun 3rd 2009, 07:51 PM
CalculusDUMMIE
Area bounded by...
Area of region bounded by the graphs of x = y^2 and x = y+ 2

graph the area bounded by y= x^2 + 1 and y = -x + 3
find the volume of the solid formed by revolving the area about the x-axis.

harder ones i assume?
graph the area bounded by x = y^2 + 1 and x = 3

graph the area bounded by x-axis, y-axis and y = e -2x in the 1st quadrant fidn teh area?

graph the area bounded by y= 1 x=4 and y = radical x..

use disc or washer method?
use integration to find the volume.

im so clueless on how to start.. i haven't been to class for a while due to surgery on my knee and missed out a lot and we are having finals soon and im so clueless.. any help would be very much appreciated thanks guys!
• Jun 3rd 2009, 08:47 PM
TKHunny

"Area Between" or "Bounded by" ...

Find the intersections and decide which is farther from the pertinent axis.

x = y^2 vs. x = y+2

Intersections:

y^2 = y + 2
y^2 - y - 2 = 0
(y-2)(y+1)=0
y = 2 or y = -1

Which is farther from the Y-Axis?

y = 0 is in the Range

0^2 = 0 and 0+2 = 2, so the linear piece is farther away.

$\displaystyle \int_{-1}^{2}(y+2)-(y^{2})\;dy$
• Jun 4th 2009, 12:30 PM
CalculusDUMMIE
yeah i guess yur right...

anyway.. can someone help out with the other problems im trying to do it and i seem to get stuck in the middle.
• Jun 4th 2009, 09:41 PM
Amer
Quote:

Originally Posted by CalculusDUMMIE

graph the area bounded by y= x^2 + 1 and y = -x + 3

do you know how to graph a curve ??

first as TKHunny said you should find the point of intersection

$\displaystyle x^2+1=-x+3$

[tex]x^2+x-2=0[tex]

$\displaystyle by..quadratic..equation$

$\displaystyle \frac{-b\mp\sqrt{b^2-4ac}}{2a}.......for......ax^2+bx+c=0....$
you know it right
you will find the points is

$\displaystyle \frac{-1+\sqrt{9}}{2}....and...\frac{-1-\sqrt{9}}{2}$

$\displaystyle the...point...of...intersection...(1)..(-2)$

do you know how to graph y=x^2 if you know to how graph it just bush it up one unit like the graph below the second one is easier

Attachment 11761

and add y=-x+3 so you will have this

Attachment 11763