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anonymous
 one year ago
Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by
y=x^3,y=16x
about the xaxis.
anonymous
 one year ago
Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^3,y=16x about the xaxis.

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0your boundaries are \(y=x^3\) and \(y=16x\) and it is rotated about the x,axis correct?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0that will look like a washer methoddw:1437943945723:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0do you know the washer method?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0(don't be ahsamed not to know, if you don't know it is ok. the only person i can not help is the silent one)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i do but have trouble with the set up

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0ok, lets figure the limits of integration together I will name them differently for our convinience \(f(x)=16x\) \(g(x)=x^3\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0lets find the points where these two functions intersect

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.016x=x³ 16=x² (and disregard negative x solutions because we are only in the 1st quadrant)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, and one more?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So our limits of integration (for the region bounded by 16x and x³) is (x=0 and x=4) \ (i.e. the intersection points after which the region stops)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So far we know \(\large\color{slate}{\displaystyle\int\limits_{0}^{4}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay got it and hw to determine inner vs outer for the formula

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, and if you were to graph the two functions \(f(x)=16x\) and \(g(x)=x^3\) then for all values on the interval [0,4] (which is the interval we need) it is true that f(x)≥g(x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So, g(x) is always below the f(x) in our case. right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0(you can test it using any value between 0 and 4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay great thanks , makes more sense now , you were a big help!!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you are thinking me already, we aren;t done yet, aren we?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i just struggle with the set up I just worked out that practice problem and solved it form there

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0ok, but, just to make sure can you show me your integral that you will set up?
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