volume problem 2

Question

volume problem 2

anonymous · Answer

attachment

anonymous · Answer

bounds y=ln x to 1

anonymous · Answer

just switch the x and y in the Y=lnx and integrate from 0 to 1 since there is no x axis limits but there is one on the y axis

anonymous · Answer

1-y = x?

anonymous · Answer

$$\pi  \int\limits_{0}^{1} (e^y)^2 dy$$

anonymous · Answer

you want your equation to be in the form x= so solve for x in the equation

anonymous · Answer

where did the e come from tho

anonymous · Answer

ohhhh cuz of ln right

anonymous · Answer

the equation is y=lnx right? so solve for x now so exponentiate both sides e^y=e^lnx so the e and the ln cancel out on the right and you are left with e^y=x

anonymous · Answer

ok ok yeah yeah blonde moment hahha

anonymous · Answer

yea so now that you are in x=e^y form you integrate up and down not left and right so it would be the integral i posted above

anonymous · Answer

well i just put that whole equation in my calc n i got a different answer then the back

tkhunny · Answer

$2\pi\int\limits_{1}^{e}x\cdot(1-\ln(x))\;dx$  Keep your mind open to other possibilities.

anonymous · Answer

wait dakota the answer is supposed to be 10. something

anonymous · Answer

did u multiply by pi? lol

tkhunny · Answer

Note: This supports and verifies dakotajason27's response if you remember to add the additional $\pi$ that I forgot.  It's about 10.036.

anonymous · Answer

oh shoot yea thanks :D

anonymous · Answer

haha no problem :b

anonymous · Answer

countless times have i forgot the pi :/