Results 1 to 4 of 4

Math Help - Integration Problems

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    3

    Integration Problems

    Maybe because it's getting late in the evening but I am lost as to how to begin these three problems:

    1. Find f(x). f'(x) = e^x - sin(x), f(0) = 1.

    2. Find s(t). s''(t) = -1, s'(0) = 3, s(0) = 7.

    3. The integral with lower limit 1 and upper limit e, (3/x)dx

    Could someone help me get these started? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by cdx9 View Post
    Maybe because it's getting late in the evening but I am lost as to how to begin these three problems:

    1. Find f(x). f'(x) = e^x - sin(x), f(0) = 1.
    f(x) = \int f'(x)~dx

    your expression for f(x) will have an arbitrary constant C. you can find this by plugging in x = 0 and setting the expression to 1, since f(0) = 1.


    2. Find s(t). s''(t) = -1, s'(0) = 3, s(0) = 7.
    similar to the last problem, you have to do the above twice.

    first find s'(t) = \int s''(t)~dt and find the arbitrary constant, then find s(t) = \int s'(t)~dt and find the arbitrary constant

    3. The integral with lower limit 1 and upper limit e, (3/x)dx

    Could someone help me get these started? Thanks!
    by the fundamental theorem of calculus, if F(x) is the anit-derivative of f(x), then

    \int_a^b f(x) = F(b) - F(a)

    i suppose you can find \int \frac 3x ~dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    3
    Thanks for the quick reply Jhevon.

    I believe I've figured out the first two problems, here is what I came up with for solutions:

    1. f(x) = e^x + cos(x) - 1

    2. s(t) = (-t^2 / 2) +3t + 7

    Feel free to correct me if those are incorrect. The third problem still eludes me. I understand the Fundamental Theorem of Calculus but the "e" in the upper limit is something I don't know how to compute. The problems/examples in my book involving e deal with indefinite integrals or definite integrals with integer values.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by cdx9 View Post
    Thanks for the quick reply Jhevon.

    I believe I've figured out the first two problems, here is what I came up with for solutions:

    1. f(x) = e^x + cos(x) - 1

    2. s(t) = (-t^2 / 2) +3t + 7
    both are correct. good job

    Feel free to correct me if those are incorrect. The third problem still eludes me. I understand the Fundamental Theorem of Calculus but the "e" in the upper limit is something I don't know how to compute. The problems/examples in my book involving e deal with indefinite integrals or definite integrals with integer values.
    e is a mathematical constant, like \pi, it is not something you compute, it has a predetermined value. it is on your calculator and everything.

    note in particular though, that \ln x means \log_e x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 3rd 2010, 12:54 AM
  2. Problems with integration word problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2010, 05:39 PM
  3. integration problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 20th 2009, 04:01 AM
  4. Integration problems
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 26th 2008, 12:02 AM
  5. Problems with some integration
    Posted in the Calculus Forum
    Replies: 21
    Last Post: July 25th 2006, 03:16 AM

Search Tags


/mathhelpforum @mathhelpforum