Question

a solid is formed by rotating y =e^x +1 between x=0 and x=3. Find the volume of the solid formed.

Answer 1

rotating about what

Answer 2

x axis ?

Answer 3

most likely, but can you have to specify

Answer 4

i suppose but question does not mention anything

Answer 5

\[= \pi \int\limits_{0}^{3} ( e^x +1)^2 dx = \pi \int\limits_{0}^{3} ( e^{2x} +2e^x +1 ) dx\]

Answer 6

\[= \pi [ \frac{1}{2} e^{2x}+ 2e^x +x ]\] between the limits

Answer 7

so what did you get as your answer?

Answer 8

\[= \pi [ ( \frac{1}{2} e^6 + 2e^3 + 3 ) - ( \frac{1}{2} +2 +0) ] = \pi [ \frac{1}{2} e^6 + 2e^3 +\frac{1}{2}] \]

Answer 9

\[= \frac{\pi}{2} [ e^6 +4e^3 +1] \]

Answer 10

i got the same answer as you but the answer provided says otherwise. it says (\[\pi/2 (e^2+1)^2u^2\]

Answer 11

any ideas on how they got that answer?

Answer 12

no, fairly sure they are wrong.

Answer 13

i'm curious about the u. where does that come from?
and i don't think it is a typo because the next questions asks
"using the substitution u=logex, find \[\int\limits_{1}^{e} loge/x .dx\]