anonymous
  • anonymous
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. y=7x^2 y^2 = (1/7)x find area of the region
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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amistre64
  • amistre64
this sounds familiar ;)
anonymous
  • anonymous
helloo and yes D: i feel like i did all the steps right, but its not the right answer >< i set both the equations to eachother to find the boundaries, thats the first step right?
anonymous
  • anonymous
7x^2 = sqrt of (1/7)x i square both sides to get rid of the radical so im left with 7x^4 = (1/7)x i multiply both sides by 7, i get 49x^4 = x subtract x from both sides, you get 49x^4 - x = 0

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amistre64
  • amistre64
can we double int it?
anonymous
  • anonymous
i believe so
amistre64
  • amistre64
y = sqrt(1/7x) y=7x^2 {SS} dy dx ; x=[0,1]; y = [7x^2,sqrt(1/7x)] right?
amistre64
  • amistre64
{S} sqrt(1/7x) - 7x^2 dx ; [0,1]
anonymous
  • anonymous
how did you get 0 and 1 ?
amistre64
  • amistre64
sqrt(1/7) 2x sqrt(x/3) - 7/x^3/3
amistre64
  • amistre64
thats where your graphs intersect at
anonymous
  • anonymous
to find the intersection, you set the equations equal to eachother right?
amistre64
  • amistre64
2sqrt(1/21)-7/3 i believe is the area
amistre64
  • amistre64
yes
amistre64
  • amistre64
did i miss that up lol
anonymous
  • anonymous
thats what i did at first, but i got x = 0 and x = cube root of 1/49
amistre64
  • amistre64
y= 7x^2; and x=7y^2
amistre64
  • amistre64
i could be wrong, trying tis in my head lol
anonymous
  • anonymous
lol youre right, but wouldnt we have to set that second equation that y is on one side by itself, not x ?
amistre64
  • amistre64
y=sqrt(1/7x) ; y = 7x^2 1/7x = 49x^4 49 x^4 - 1/7x = 0 x(49x^3 - 1/7) = 0 x=0 to.....my brain shut off lol
anonymous
  • anonymous
1/7x(343x^3 - 1) = 0
anonymous
  • anonymous
x = 0 and x = cube root of 1/343 ?
amistre64
  • amistre64
wolfram tells me that (1,1/7) is the solution to these; lets try that out :)
amistre64
  • amistre64
sqrt(1/7*1) = sqrt(1/7) 7*1 = 7....... ack!!
anonymous
  • anonymous
lol xD
anonymous
  • anonymous
hmm
amistre64
  • amistre64
deep breath....... ok
amistre64
  • amistre64
y=7x^2 and y^2 = 1/7x right?
anonymous
  • anonymous
yup
amistre64
  • amistre64
we know zero is a good one
anonymous
  • anonymous
yes
amistre64
  • amistre64
y =1 1 7 ---- = 1/7; at x=1/7, y = 1/7 ; thats y=x^2 7 7
amistre64
  • amistre64
at x = 1/7; we get y = sqrt(1/7 1/7) = sqrt(1/49) = 1/7
amistre64
  • amistre64
so lets int this thing from 0 to 1/7 :)
anonymous
  • anonymous
im sorry im a little lost, how did you get 1/7 for x ?
amistre64
  • amistre64
[S] 7x^2 - sqrt(1/7x) dx ; [0,1/7] ....i guessed and was right :)
anonymous
  • anonymous
xD awesome haha
amistre64
  • amistre64
i had an inclination, but couldnt verify it till i just plugged it in ;)
amistre64
  • amistre64
i know that this is 2 parabolas at right angles to each other; so they only meet at 2 point, to that one works and has to be it lol
amistre64
  • amistre64
7x^3/3 - 2sqrt((7x)^3)/3 ??
anonymous
  • anonymous
is the 2aqrt((7x)^3)/3 the same as 2x^(3/2) divided by 21 ? cuz i put sqrt of 1/7 as (1/7)^(1/2) and found the antiderivative like that
amistre64
  • amistre64
sqrt(1/7)* sqrt(x) = sqrt(1/7)* 2sqrt(x^3)/3 7x^3/3 - 2sqrt(1/7x^3)/3 right?
amistre64
  • amistre64
the sqrt(1/7) is actually a constant, so we can pull it out of the way and just do sqrt(x)
amistre64
  • amistre64
sqrt(ab) = sqrt(a) * sqrt(b)
anonymous
  • anonymous
ohhh i see
amistre64
  • amistre64
1/49(3) - 2sqrt(1/7^4)/3 should be the area
anonymous
  • anonymous
how comes its (1/7^4) ?
amistre64
  • amistre64
1 2sqrt(1/2401) --- - ------------ 147 3 (1/7) * (1/7)^3 = 1/7^4
amistre64
  • amistre64
as long as i integrated it right, and im pretty sure i did :)
amistre64
  • amistre64
dbl check it tho ;)
anonymous
  • anonymous
im going over it right now :D
amistre64
  • amistre64
\[\int\limits_{} (7x^2 - \sqrt{\frac{1}{7}x} )dx\]
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=int%287x^2+-sqrt%28x%2F7%29%29dx++from+0+to+1%2F7
amistre64
  • amistre64
id take the absolute value of that :)
anonymous
  • anonymous
thats what i got too :) and i jus ttake the absolute value of that since its negative right ?
amistre64
  • amistre64
correct; just means we got the wrong order
amistre64
  • amistre64
see...http://www.wolframalpha.com/input/?i=int%28sqrt%28x%2F7%29-7x^2%29dx++from+0+to+1%2F7
anonymous
  • anonymous
gotcha. thank you once again. always coming to my rescue :D haha youre the best !

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