Results 1 to 4 of 4
Like Tree2Thanks
  • 2 Post By HallsofIvy

Math Help - Exponential Functions and Integrals

  1. #1
    Newbie
    Joined
    May 2013
    From
    I don't even know
    Posts
    2

    Exponential Functions and Integrals

    I have a test tomorrow and I'm not getting the answers on a study guide for a couple and I forgot how I did another and lost all my understanding.

    These are the formulas I was given: http://i.imgur.com/6rwL0S6.jpg

    This is #4 (which I got close to the answer but not the entire thing): http://i.imgur.com/NaJhF5Y.jpg
    My work: http://i.imgur.com/l8OHuCD.jpg

    This is #9 (where again I got close to the answer but it's not negative): http://i.imgur.com/irn4fUd.jpg
    My work: http://i.imgur.com/VGdxQkx.jpg


    This is #11 (which I've done before but looking at it again I'm very confused and have no understanding of my work. It'd be nice if someone could show me this one step by step): http://i.imgur.com/8RKTBfe.jpg
    My work: http://i.imgur.com/nexHgNv.jpg

    These are the answers: http://i.imgur.com/qXXNP0j.jpg

    Thanks in advance.
    Last edited by cperzely; May 28th 2013 at 06:07 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,057
    Thanks
    1685

    Re: Exponential Functions and Integrals

    Quote Originally Posted by cperzely View Post
    I have a test tomorrow and I'm not getting the answers on a study guide for a couple and I forgot how I did another and lost all my understanding.

    These are the formulas I was given: http://i.imgur.com/6rwL0S6.jpg

    This is #4 (which I got close to the answer but not the entire thing): http://i.imgur.com/NaJhF5Y.jpg
    My work: http://i.imgur.com/l8OHuCD.jpg
    What you give as the "correct answer", \frac{x- 2}{(ln(2))x(x-1)} is NOT equal to \frac{2}{ln(2)x}- \frac{1}{ln(2)(x- 1)}. You appear to have done the "partial fractions" incorrectly.

    This is #9 (where again I got close to the answer but it's not negative): http://i.imgur.com/irn4fUd.jpg
    My work: http://i.imgur.com/VGdxQkx.jpg
    The formula you are given is for \int a^x dx but the problem is \int 4^{-x} dx. Either use the substitution u= -x or write the problem as \int (4^{-1})^x dx= \int \left(\frac{1}{4}\right)^x dx

    This is #11 (which I've done before but looking at it again I'm very confused and have no understanding of my work. It'd be nice if someone could show me this one step by step): http://i.imgur.com/8RKTBfe.jpg
    My work: http://i.imgur.com/nexHgNv.jpg
    Use the substitution u= (3- x)^2

    These are the answers: http://i.imgur.com/qXXNP0j.jpg

    Thanks in advance.
    Thanks from topsquark and cperzely
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2013
    From
    I don't even know
    Posts
    2

    Lightbulb Re: Exponential Functions and Integrals

    Thank you for the help HallsofIvy. I redid #11 again and got the answer but did I solve this in a more difficult way than I needed too? I first substituted for 3-x then substituted again for u^2: http://i.imgur.com/wACU8yG.jpg

    Also here's the formula I used for this one (as well as for #4): http://i.imgur.com/5A6nktd.jpg
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member x3bnm's Avatar
    Joined
    Nov 2009
    Posts
    300
    Thanks
    16

    Re: Exponential Functions and Integrals

    Like HallsofIvy said:

    Let u = (3-x)^2\,\, \therefore \mathrm{d}u = -2(3-x)\,\,\mathrm{d}x

    Now the integral becomes:

    \int (3 -x)7^{(3-x)^2}\,\,\mathrm{d}x = -\frac{1}{2}\int 7^u\,\, \mathrm{d}u

    Now you can finish the rest using the formula you mentioned in your last post.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 13th 2013, 07:18 AM
  2. Replies: 2
    Last Post: June 9th 2011, 09:54 AM
  3. Integrals involving exponential
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2010, 03:47 AM
  4. Replies: 4
    Last Post: February 10th 2009, 09:54 PM
  5. Help with Natural exponential integrals
    Posted in the Calculus Forum
    Replies: 10
    Last Post: June 25th 2007, 06:53 PM

Search Tags


/mathhelpforum @mathhelpforum