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pdd21
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Calc Problem: Help please!
Find the volume of the solid obtained by rotating the region bounded by y=9 x^2, x = 1, and y = 0, about the xaxis.
 10 months ago
 10 months ago
pdd21 Group Title
Calc Problem: Help please! Find the volume of the solid obtained by rotating the region bounded by y=9 x^2, x = 1, and y = 0, about the xaxis.
 10 months ago
 10 months ago

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pdd21 Group TitleBest ResponseYou've already chosen the best response.0
@campbell_st
 10 months ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
ok the the formula for rotating about the x axis is \[V = \pi \int\limits_{a}^{b} y^2 dx\] so the values of a and b are and then y = 0 the corresponding value of x is x = 0... so that means a = 0 and b = 1 the graph looks like dw:1386823443784:dw so you are looking at \[V = \pi \int\limits_{0}^{1} (9x^2)^2 dx\] so just simply the (9x^2)^2 then integrate and evaluate between x = 1 and x = 0
 10 months ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
hope this helps
 10 months ago

pdd21 Group TitleBest ResponseYou've already chosen the best response.0
Thank you so much that helped clear up my confusion! there was another problem I was stuck on, but instead of it being respect to xaxis it's respect to the yaxis. > Find the volume of the solid obtained by rotating the region bounded by y=x^2 , y = 0, and x = 3, about the yaxis. how do I solve this problem? @campbell_st
 10 months ago

pdd21 Group TitleBest ResponseYou've already chosen the best response.0
Do i solve it the same?
 10 months ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
ok... so find the upper value of the curve at x = 3 so y = 9 this is similar to before dw:1386823955174:dw the values of a and b are a = 0 and b = 9 so you are looking at \[V = \pi \int\limits_{a}^{b} x^2 dy\] you have your equation in terms of x^2 so its \[V = \pi \int\limits_{0}^{9} y dy\] hope it makes sense
 10 months ago

pdd21 Group TitleBest ResponseYou've already chosen the best response.0
so, \[V=\pi \int\limits_{0}^{9} (x^2)\] I don't seem to be getting the correct answer ;/ @campbell_st
 10 months ago

pdd21 Group TitleBest ResponseYou've already chosen the best response.0
nvm! I caught my mistake! haha
 10 months ago

pdd21 Group TitleBest ResponseYou've already chosen the best response.0
Thankk you!(:
 10 months ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
well because you are rotating about the y axis you integrate with respect to y \[V = \pi \int\limits_{0}^{9} y dy = 2\pi[\frac{y}{2}]^9_{0}\]
 10 months ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
oops forgot the y^2... \[V = \pi \int\limits_{0}^{9} y dy = \pi [\frac{y^2}{2}]^9_{0}\]
 10 months ago
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