Calculus Question PLEASE HELP!!!

[jpage447]

Integration Calculus Question PLEASE HELP!!!

I am working on my Calculus take home packet and there is one part of a short answer which I don't know how to answer.

The question refers to the region R enclosed by the x-axis, y-axis, the line x=2, and the curve y=2e^x+3x
For part (b) i am told to "find the volume of the solid generated by revolving R about the Y-axis by setting up and evaluating a definite integral. Your work must include the antiderivative."

So, i plan on using the shell method, so i know that when i set up the integral it would look like:

I know how to put this in my calculator (TI-84 plus)to get an answer(which is equivalent to), but my teacher wants the antiderivative and i haven't been able to find how to integrate by hand. so...
HOW DO I INTEGRATE THIS BY HAND???? I DON'T NEED THE NUMERICAL ANSWER, I JUST WANT THE ANTIDERIVATIVE!!!

:???:

 

[daon2]

Your trouble is probably this integral:

\(\displaystyle \displaystyle \int_0^2 xe^x dx\).

This is done by parts. Let \(\displaystyle u = x, \frac{dv}{dx}=e^x\).

 

[jpage447]

i'm still confused

Your trouble is probably this integral:

\(\displaystyle \displaystyle \int_0^2 xe^x dx\).

This is done by parts. Let \(\displaystyle u = x, \frac{dv}{dx}=e^x\).

What do you mean i do it by parts. and where does dv/dx come from? i'm sorry i'm still confused. can you expand you explanation please?

 

[daon2]

What do you mean i do it by parts. and where does dv/dx come from? i'm sorry i'm still confused. can you expand you explanation please?

If you have been instructed to find this integral by hand, your professor should have either

1) Covered integration by parts
2) A reasonable expectation that your previous class has covered integration by parts.

If you choose to use the washer method you will not escape this either, unfortunately. I suggest you review this section in your textbook.

 

[Deleted member 4993]

What do you mean i do it by parts. and where does dv/dx come from? i'm sorry i'm still confused. can you expand you explanation please?

Just in case you forgot:

\(\displaystyle \displaystyle \frac{d}{dx} \left [u(x) * v(x)\right ] = u(x) * \frac{d}{dx} v(x) \ + \ v(x) * \frac{d}{dx} u(x) \)

from which we get,

\(\displaystyle \displaystyle \int u(x) * \left [\frac{d}{dx}v(x)\right ] dx = u(x) * v(x) - \int v(x) * \left [\frac{d }{dx}u(x)\right ] dx\).

 

[jpage447]

OOOOOOh thanks!

Just in case you forgot:

\(\displaystyle \displaystyle \frac{d}{dx} \left [u(x) * v(x)\right ] = u(x) * \frac{d}{dx} v(x) \ + \ v(x) * \frac{d}{dx} u(x) \)

from which we get,

\(\displaystyle \displaystyle \int u(x) * \left [\frac{d}{dx}v(x)\right ] dx = u(x) * v(x) - \int v(x) * \left [\frac{d }{dx}u(x)\right ] dx\).

yeah lol i forgot the formula for integrating by parts. Thanks! i got it now!

 

[daon2]

I haven't been in school for the past 10 days im on vacation so she probably taught it to us while i was gone. If i was asking for someone to remind me that my teacher teaches us about calculus i would have asked a different question. There's no point in posting a response to someone's question if your not going to help them reach an answer. THe website is called "freemathhelp.com", not rudecomments.com

If you ask me, it is your comment that is rude. I did help you, and if you were a competent student you would have realized that much.

 

[daon2]

You are obviously here to answer questions and provide help, since that is what the website is for, so when someone is asking you to better explain a response you either do it or you don't;there is no need to provide unhelpful answers. If you do not intend to help someone acquire a better understanding of whatever they are asking about, then you have no place replying to the post.

I correctly identified the issue you were having, and I started the process of integration by parts for you. When I realized you have never heard of it before, I suggested that it should have been covered, as it is necessary to perform this integral. I then pointed you to your textbook. Why is it expected of a volunteer to retype the material in your book? Also, a lesson for integration by parts is automatically linked in the post I made by this website.

By competency, I was referring to you ignoring my clear suggestion to (re)view a certain technique to remedy your problem. Instead you deemed my post unhelpful because I "reminded you that your teacher teaches you about calculus." What? Is it so hard to say "there's something I do not know, so I should open the book!"

Even more confusing is stating you have never heard of it before, and then saying "oh yeah i forgot it".

 

[Deleted member 4993]

I haven't been in school for the past 10 days im on vacation so she probably taught it to us while i was gone. If i was asking for someone to remind me that my teacher teaches us about calculus i would have asked a different question. There's no point in posting a response to someone's question if your not going to help them reach an answer. THe website is called "freemathhelp.com", not rudecomments.com

When you come in asking for "help" - and you have been reminded of a deficiency in your background - take it as a chance to improve yourself.