Question

The linear density p in a rod 5 m long is 10/sqrt(x+4) kg/m, where x is measured in meters from one end of the rod. Find the average density of the rod. pave=? kg/m

Answer 1

@dumbcow

Answer 2

you are given equation for density over an interval to find avg use this
\[avg = \frac{1}{b-a} \int\limits_a ^b f(x) dx\]
\[\frac{1}{5} \int\limits_0^5 \frac{10}{\sqrt{x+4}} dx\]

Answer 3

so how does the P work into this?

Answer 4

not sure, i think its a label for density.... p = f(x) but it has no bearing on avg density

Answer 5

I thought the question was saying it had to be plugged in somewhere. Thats what was throwing me haha

Answer 6

no the key is "x' is length from end of rod so you know you have to integrate wrt "x"

Answer 7

any problems integrating this? pretty straightforward with a "u" substitution

Answer 8

oh ok i see where you are coming from

Answer 9

naaa i got the integrating thing down now lol its just always the set up thats gets me

Answer 10

gotcha

Answer 11

Thank you!

Answer 12

yw

Answer 13

i got 4 as an answer

Answer 14

correct

http://www.wolframalpha.com/input/?i=integrate+2%2Fsqrt%28x%2B4%29+from+0+to+5
useful tool for checking answers

Answer 15

sweet I actually have another question just want you to tell me if im setting it up right

find the average value of the function h on the interval.
h(x)=6cos^4 x sin x [0.pi]

the integral if just \[\frac{ 1 }{ \pi }\int\limits_{0}^{\pi}6\cos^4xsinx \]

Answer 16

looks good

Answer 17

ok i think im starting to get this

Answer 18

Now all i need to get is those cylindircal shells and i can take the test lol

Answer 19

oh yeah have you learned shell method now

Answer 20

yep Use the method of cylindrical shells to find the volume of the solid obtained by rotatin the region bounded by the given curves about the x-axis.

xy=5 x=0 y=5 y=7

so x=5/y

\[\int\limits_{5}^{7}(2\pi y)(5/y) = 20\pi\]

i think.... lol

Answer 21

hold on let me draw it out lol

Answer 22

ok you got it

Answer 23

:D happy danceeee

Answer 24

ok will you check one more for me? find the volume v of the described solid S. The base of S is a circular disk with radius 5r. Parallel cross sections perpendicular to he base are squares. i got V=2000/3 r^3

Answer 25

i believe you are right :)

sum up all the areas....area of square is 4y^2...put y in terms of x ....

Answer 26

Perfect :) you rock my friend

Answer 27

thank you...looks like you got the hang of it, keep practicing

Answer 28

here is link to good reference site with notes/examples/practice problems

http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx

Answer 29

ohhhh nice I hope it has something about J thats my new challenge lol