Results 1 to 11 of 11

Math Help - integration homework help

  1. #1
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    integration homework help

    I rewrote this as

    = t(t - 4)^1/3.... do I combine them and integrate after?
    Attached Thumbnails Attached Thumbnails integration homework help-screen-shot-2012-12-11-9.13.55-am.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Dec 2012
    From
    Danmark
    Posts
    11
    Thanks
    4

    Re: integration homework help

    Integration by parts, like the other one i commented on u(x)=(t-4)^(1/3), v(x)=t
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426

    Re: integration homework help

    \int t \sqrt[3]{t-4} \, dt

    u = t-4

    t = u+4

    du = dt

    substitute ...

    \int (u+4) \cdot \sqrt[3]{u} \, du

    can you finish?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Dec 2012
    From
    Danmark
    Posts
    11
    Thanks
    4

    Re: integration homework help

    ...or that XD
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    Re: integration homework help

    this is different on how i learned it.... so i integrate the right side??? sorry idk x/
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Nov 2012
    From
    Hawaii
    Posts
    260
    Thanks
    2

    Re: integration homework help

    wait i got it... im working on it at the moment....
    okay heres what i've got so far

    u = t - 4
    du = dt
    t = u + 4

    = ^3√u ( u + 4) + c
    = u^1/3 (u + 4) + c

    now do i multiply u^1/3 (u + 4) together and integrate?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,402
    Thanks
    1291

    Re: integration homework help

    Yes.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member x3bnm's Avatar
    Joined
    Nov 2009
    Posts
    300
    Thanks
    16

    Re: integration homework help

    \text{We know that } \int u \, dv=uv-\int v \, du.\!

    So for \int t\sqrt[3]{t-4} \;\;dt let u = t \therefore du = dt
    And let dv = \sqrt[3]{t-4} \;\;dt \therefore v = \frac{3}{4}(t - 4)^{\frac{4}{3}}

    \begin{align*}\int t\sqrt[3]{t-4} \;\;dt =& \frac{3}{4}t(t-4)^{\frac{4}{3}} - \int \frac{3}{4}(t - 4)^{\frac{4}{3}} \\ =& \frac{3}{4}t(t-4)^{\frac{4}{3}} - \frac{9}{28}(t-4)^{\frac{7}{3}} + C \\ =& \frac{3}{7}(t-4)^{\frac{4}{3}}[\frac{7t}{4} - \frac{3t}{4} + \frac{12}{4}] + C \\ =& \frac{3}{7}(t-4)^{\frac{4}{3}}(t+3) + C\end{align*}

    \therefore \int t\sqrt[3]{t-4} \;\;dt = \frac{3}{7}(t-4)^{\frac{4}{3}}(t+3) + C

    Check:

    int x(x-4)^(1/3) dx - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member
    Joined
    Mar 2010
    Posts
    980
    Thanks
    236

    Re: integration homework help

    Or starting from skeeter's post,

    \int (u+4) \cdot \sqrt[3]{u} \, du =\int u^\frac{4}{3} + 4u^\frac{1}{3} \, du =

    \frac{3}{7}u^\frac{7}{3}+ 3 u^\frac{4}{3} + C = \frac{3}{7}u^\frac{4}{3} (u + 7) + C=

    \frac{3}{7} (t-4)^\frac{4}{3} (t+3) + C


    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Mar 2013
    From
    USA
    Posts
    18

    Re: integration homework help

    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,367
    Thanks
    1312

    Re: integration homework help

    Quote Originally Posted by asilvester635 View Post
    wait i got it... im working on it at the moment....
    okay heres what i've got so far

    u = t - 4
    du = dt
    t = u + 4

    = ^3√u ( u + 4) + c
    = u^1/3 (u + 4) + c

    now do i multiply u^1/3 (u + 4) together and integrate?
    You have not yet integrated so there should be no "+ c".
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Homework help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 16th 2012, 05:09 AM
  2. Homework help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 13th 2009, 10:40 AM
  3. Integration Problem for Calculus Homework
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 22nd 2009, 12:06 AM
  4. Help with son's homework
    Posted in the Statistics Forum
    Replies: 2
    Last Post: February 8th 2008, 06:21 PM
  5. Homework HELP
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 28th 2006, 08:03 PM

Search Tags


/mathhelpforum @mathhelpforum