anonymous
  • anonymous
The region R is bounded by the x-axis and the graphs of y=2-x^3 and y=tan(x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
I need to find the area of R
anonymous
  • anonymous
I got the graph part. I just need to find the area of that part.
anonymous
  • anonymous
this requires the coordinates of point P by solving the equation 2 - x^3 = tanx |dw:1333521423411:dw|

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anonymous
  • anonymous
how would you do that?
anonymous
  • anonymous
i figured you'd know... I don't think there's an elementary algebra technique to solve that equation... you might need the help of a graphing calculator...
anonymous
  • anonymous
what part of the graphing calculator would help me with this?
anonymous
  • anonymous
finding the intersection of two graphs.... in this case y = tanx and y = 2-x^3
anonymous
  • anonymous
i would use zoom box on the graphing calculator
anonymous
  • anonymous
yes, but be care with using the functions of a graphing calculator... let the calculator find the intersection for you and not you zooming in on the intersection until you find it. what kind of calculator are you using?
anonymous
  • anonymous
TI-84 PLus
anonymous
  • anonymous
How would I let calculator find the intersection points?
anonymous
  • anonymous
go to "y=" and in y1 enter tan (x) y2 enter 2 - x^3
anonymous
  • anonymous
lemme know when you're done...
anonymous
  • anonymous
I did that then i hit zoom box until i got close enough then I used the trace button to get as close to the intersection
anonymous
  • anonymous
yeah that's what I mean about not doing that because the calculator can give you a better approximation of the intersection...
anonymous
  • anonymous
wait... make sure you're in "radian" mode.
anonymous
  • anonymous
yes im in radians and I entered the y1 and y2
anonymous
  • anonymous
ok, now press 2ND - CALC - 5 (intersect)
anonymous
  • anonymous
enter, enter, enter
anonymous
  • anonymous
o so thats how you do that!!!
anonymous
  • anonymous
calculator should give you x = .90215 y = 1.2657 is that what you got?
anonymous
  • anonymous
yes so those points what go in my integral
anonymous
  • anonymous
yes. you'll use the lower limit of 0 and upper limit of 1.2657...
anonymous
  • anonymous
since you're using the calculator you might as well let the calculator find the area for you.. wanna see how it's done?
anonymous
  • anonymous
i know that part already but how you set up the problem for R bounded by the x-axis and S bounded by the y-axis
anonymous
  • anonymous
what's S? the problem only wanted region R as I put in the drawing....
anonymous
  • anonymous
tehn it asks for region S which is bounded by the y-axis at the same points
anonymous
  • anonymous
|dw:1333522896129:dw| that's region S? and you want the area for it?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok|dw:1333523054819:dw| can we just take the whole area under y=2-x^3, take the area of S, then to get R, we subtract S from the whole area... or do you want separate integrals for the area of R and S separately?
anonymous
  • anonymous
seperately because thats how my teacher wants it
anonymous
  • anonymous
ok, let's do R first then since that's what was asked first. notice that the representative rectangle is laying down so the width of that rectangle is dy and the height is obtained by [right curve] - [left curve].
anonymous
  • anonymous
you must solve for x in both y=tanx and y=2-x^3....
anonymous
  • anonymous
so just put the integral in the calculator by (2-x^3)-(tan(x))dx
anonymous
  • anonymous
no, you must solve for x first.... in both curves....
anonymous
  • anonymous
|dw:1333523725608:dw| the reason you need to solve for x for both equations is because you need h to find the representative area dA.
anonymous
  • anonymous
so how you do that?? x=3squareroot of 2 tanx=?
anonymous
  • anonymous
|dw:1333523991360:dw|
anonymous
  • anonymous
|dw:1333524156076:dw| there's your area for R.... S should be easier because your taking dx and your height is top function - bottom function...
anonymous
  • anonymous
o i did it wrong
anonymous
  • anonymous
can you find area of dy by using the calculator
anonymous
  • anonymous
i got .729 un 2 so how you set up S
anonymous
  • anonymous
.729 for the area of R? lemme check...
anonymous
  • anonymous
yep that's what I got too... .729 :)
anonymous
  • anonymous
now S?
anonymous
  • anonymous
ok
anonymous
  • anonymous
|dw:1333524733187:dw| that's S on the lower left....