Calculating Volume with the Shell Method for Enclosed Region

[prox9]

I used to be able to do stuff like this when i was in high school but now I am in college and i can't do basic stuff like this. the problem this sub problem is from is

Find the volume of the solid formed by rotating the region enclosed by
y=e^{ x} + 5, \ y=0, \ x=0, \ x=0.1

Im trying to solve it with the shell method but i can't seem to get it right

I thought should be the integral from 0 to .1 of (xe^x)+(5x) and then times 2pi for the # in front of the integral.

 

[radou]

Try times 2*0.1*Pi in front of the integral.

 

[prox9]

psh my bad the answer was .19067 and not .19037. I hate doing work online for a class where the professor wastes 40 minutes explaining the stupid theorem behind why the shell method works when she could have just put the formula up and i would have gotten it right away. Maybe I am just dumb but i got a 5 on the ap calculus exam and the highest grade in the class both semesters. Why do the professors waste so much time on pointless crap?

 

[d_leet]

Try times 2*0.1*Pi in front of the integral.

Why? (more characters)

 

[HallsofIvy]

psh my bad the answer was .19067 and not .19037. I hate doing work online for a class where the professor wastes 40 minutes explaining the stupid theorem behind why the shell method works when she could have just put the formula up and i would have gotten it right away. Maybe I am just dumb but i got a 5 on the ap calculus exam and the highest grade in the class both semesters. Why do the professors waste so much time on pointless crap?

Yes, it's terrible when professors expect you to learn something instead of just memorizing formulas. Why that would involve thinking!

 

[prox9]

Maybe, it's the fact that she has a thick accent and every seat except the front center seats can't read the majority of the stuff she writes on the board since the classroom is big and flat and not sloped as it should be for a class that size. Though I probably shouldn't complain given that this is low math compared to what I'm going to have to do later on.

 

[radou]

Why? (more characters)

I assumed rotation around the y-axis. If it's rotation around the x-axis, then \pi \int_{0}^{0.1}(e^x+5)^2dx is used.

 

[HallsofIvy]

Maybe, it's the fact that she has a thick accent and every seat except the front center seats can't read the majority of the stuff she writes on the board since the classroom is big and flat and not sloped as it should be for a class that size. Though I probably shouldn't complain given that this is low math compared to what I'm going to have to do later on.

Then make sure you get a set in the front center! When I was a freshman, I had a teacher who talked about "delters" and "epsilons". I couldn't complain- it was in Boston and that's their language. When I was in graduate school I had a teacher from Cuba. A friend asked if she could copy the teacher's notes (he taught from several pages of notes!) but they were all in Spanish!

 

[HallsofIvy]

Maybe, it's the fact that she has a thick accent and every seat except the front center seats can't read the majority of the stuff she writes on the board since the classroom is big and flat and not sloped as it should be for a class that size. Though I probably shouldn't complain given that this is low math compared to what I'm going to have to do later on.

Then make sure you get a seat in the front center! When I was a freshman, I had a teacher who talked about "delters" and "epserlons". I couldn't complain- it was in Boston and that's their language. When I was in graduate school I had a teacher from Cuba. A friend asked if she could copy the teacher's notes (he taught from several pages of notes!) but they were all in Spanish!

Now, I teach in sign language, my students are all deaf or hard of hearing and they have to put up with my "accent"!

 

[d_leet]

I assumed rotation around the y-axis. If it's rotation around the x-axis, then \pi \int_{0}^{0.1}(e^x+5)^2dx is used.

But the original post specifically said that the shell method was being used and not rotation about either axis.

 

[FunkyDwarf]

intergration by parts is your friend, at least for the first bit. the second bit you can, as I am sure you know, do seperately

oh and i think the previous posters are missing the x infront of the exponential, or I am missing something you guys said

 

[radou]

But the original post specifically said that the shell method was being used and not rotation about either axis.

Sorry. Wasn't familiar with the term 'shell method'.