Results 1 to 10 of 10

Math Help - Solve Integral with TI-84 Plus

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    24

    Solve Integral with TI-84 Plus

    It's been a long time since I've done any calculus, so I've forgotten how to use my calculator to solve integrals. I have to solve

    \int_1^x \! (1/t) \, \mathrm{d}t

    for a few different x values. How can I do this using a graphing calculator (TI-84 Plus)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by kwikness View Post
    It's been a long time since I've done any calculus, so I've forgotten how to use my calculator to solve integrals. I have to solve

    \int_1^x \! (1/t) \, \mathrm{d}t

    for a few different x values. How can I do this using a graphing calculator (TI-84 Plus)?
    You need a Ti - 89.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    24
    Quote Originally Posted by dwsmith View Post
    You need a Ti - 89.
    A TI-84+ is recommended for the course. Here is the problem out of the book:
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by kwikness View Post
    A TI-84+ is recommended for the course. Here is the problem out of the book:
    Unless they have changed those calculators, they can't integrate with respect to a variable. If you had and integral bounded by values not at an asymptote, you could graph it, hit calculate, select integrate, and put in the bounds.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Hi there, you are not required to evaluate that integral.

    You need to make a table in the Ti-84 to solve the approximation of the intergal using simpson's rule.

    Do you know what this rule is?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2008
    Posts
    24
    Quote Originally Posted by pickslides View Post
    Hi there, you are not required to evaluate that integral.

    You need to make a table in the Ti-84 to solve the approximation of the intergal using simpson's rule.

    Do you know what this rule is?
    I looked up Simpson's rule, but I'm not sure how to apply it to doing this problem with a calculator. Does anyone have any advice?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by kwikness View Post
    I looked up Simpson's rule,
    Is this the rule?

    \displaystyle \int_a^b f(x)~dx \approx \frac{b-a}{6}\left[ f(a)+4f\left(\frac{b-a}{2}\right)+f(b)\right]

    If so you are given different upper bounds in the first row of the table.

    For x = 0.5 then \displaystyle \int_1^{0.5} f(x)~dx \approx \frac{0.5-1}{6}\left[ f(1)+4f\left(\frac{0.5-1}{2}\right)+f(1)\right]=\dots

    Using the calculator gives you the power to evaluate all these sums at the same time.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by pickslides View Post
    Is this the rule?

    \displaystyle \int_a^b f(x)~dx \approx \frac{b-a}{6}\left[ f(a)+4f\left(\frac{b-a}{2}\right)+f(b)\right]

    If so you are given different upper bounds in the first row of the table.

    For x = 0.5 then \displaystyle \int_1^{0.5} f(x)~dx \approx \frac{0.5-1}{6}\left[ f(1)+4f\left(\frac{0.5-1}{2}\right)+f(1)\right]=\dots

    Using the calculator gives you the power to evaluate all these sums at the same time.
    That is Simpson's rule for n=2

    The OP asked for Simpson's rule with n=10

    In general we have

    n must be even and \displaystyle \Delta x=\frac{b-a}{n}

    x_i=a+i\Delta x, i=0,1,2,...,n

    \displaystyle \int_{a}^{b}f(x)dx=\frac{\Delta x}{2}\left[ f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+2f(x_{n-2}+4f(x_{n-1})+f(x_n)\right]
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Sep 2008
    Posts
    24
    Quote Originally Posted by TheEmptySet View Post
    That is Simpson's rule for n=2

    \displaystyle \int_{a}^{b}f(x)dx=\frac{\Delta x}{2}\left[ f(x_0)+4f(x_1)+2f(x_2)+4f(x_3)+...+2f(x_{n-2}+4f(x_{n-1})+f(x_n)\right]

    • How do I determine what to put in the denominator under delta x?
    • How do I get past leaving a 0 in the denominator when I evaluate X of 0? f(x_0) = 1/0
    • Also, I'm having trouble figuring out what the best way to evaluate this on a calculator would be. I have to evaluate it at .5, 1.5, ...
    Last edited by kwikness; February 13th 2011 at 04:25 PM.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    454
    Simpson's rule to approximate the value of a definite integral ...



    for x = 0.5 ...

    \Delta x=\dfrac{0.5-1}{10} = -.05

    \displaystyle \int_{1}^{0.5} \frac{1}{t} \, dt \approx \frac{-0.05}{3}\left[ \frac{1}{1}+4 \cdot \frac{1}{.95} + 2 \cdot \frac{1}{.90} + 4 \cdot \frac{1}{.85} + 2 \cdot \frac{1}{.80} + 4 \cdot \frac{1}{.75} + 2 \cdot \frac{1}{.70} + 4 \cdot \frac{1}{.65} + 2 \cdot \frac{1}{.60} + 4 \cdot \frac{1}{.55} + \frac{1}{.50}\right] = -0.6931502307

    now do the same for every x-value (upper limit of integration) in the table.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solve the following integral:
    Posted in the Math Challenge Problems Forum
    Replies: 12
    Last Post: January 18th 2011, 12:48 PM
  2. Replies: 1
    Last Post: June 9th 2009, 10:37 PM
  3. Integral I can't solve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 17th 2009, 05:44 PM
  4. How to solve this integral?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 4th 2008, 10:52 AM
  5. How do you solve this integral?
    Posted in the Calculus Forum
    Replies: 6
    Last Post: August 8th 2008, 05:13 PM

Search Tags


/mathhelpforum @mathhelpforum