Question

A region bounded by f(x) = sqrt(x + 4) , y = 0, x = -3, and x = 0 is shown below. Find the volume of the solid formed by revolving the region about the x-axis.

Answer 1

http://assets.openstudy.com/updates/attachments/51aa2b01e4b0ffa8e49bb250-onegirl-1370106633946-calc_final_semester_b_220q2.gif

Answer 2

since it's bound by x=-3 and x=0, y=0 \[\large f(x)=\sqrt{x+4}\]\[\large y=\sqrt{x+4}\]\[\large A=\pi(\sqrt{x+4})^2\]\[\large A=\pi(x+4)\]Now we're finding volume,and you can find it by integrating this area we've found. \[\large V=\pi \int\limits_{-3}^{0}Adx\]\[\large V=\pi \int\limits_{-3}^{0}(x+4)dx\]\[\large V=\pi[x^2+4x]\] integrate from -3 to 0\[\large V=\pi[((0)^2+4(0))-((-3)^2+4(-3))]\]Simplify

Answer 3

hmm i get 3pi but 3pi isn't in the choices

Answer 4

@Jhannybean

Answer 5

my answer choices are

a. 15/2 pi
b. 16pi
c. 17/2pi
d. 11pi

Answer 6

@Jhannybean

Answer 7

@Luigi0210

Answer 8

Not volume D:

Answer 9

and the reason being cause Miss @Jhannybean made a booboo

Answer 10

ohh ok

Answer 11

sooo can u help?

Answer 12

Do you see where she took the anti-derivative and got x^2+4x?

Answer 13

yes

Answer 14

Well she forgot to put it over 2 :P
because \[\int\limits xdx=\frac{ x^2 }{ 2 } +C\]

Answer 15

Now solve it and see what you get

Answer 16

Did you get it? @onegirl

Answer 17

yes sorry

Answer 18

so x^2 + 4x^2 ? or

Answer 19

No you are using \[\Pi[\frac{ x^2 }{ 2 }+4x] \]

Answer 20

ohhh ok thanks :D

Answer 21

Yup, it was all thanks to @Jhannybean .. without her equation we'd be lost :l

Answer 22

yea BUT i get -27/2 and its not in my answer choices :/

Answer 23

How did you get that?
I got something different

Answer 24

you did? :/ i used WA

Answer 25

WA?

Answer 26

wolfram alpha

Answer 27

\[\Pi([0]-[\frac{ (-3)^2 }{ 2 }+4(-3)]\])
\[\Pi [0-(\frac{ 9 }{ 2 }-12)]\]
\[\Pi[0-(\frac{ -15 }{ 2 })]\]
\[\frac{ 15 }{ 2 }\Pi\]

And oh, maybe you should try using your brain.. those things are wrong at times

Answer 28

okay

Answer 29

Hope that made sense ^_^'

Answer 30

oh hahaha -_- i forgot the two... darn.