Results 1 to 11 of 11

Math Help - anti-derivative problems

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    8

    Exclamation anti-derivative problems

    hi guys, i need help finding the anti-derivatives for these problems

    Any help woud be appreciated

    y' = tan(x)sec^2(x)

    y' = 3x^(-1/2)

    y' = -2cot^2(x)csc(x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by sess View Post
    hi guys, i need help finding the anti-derivatives for these problems

    Any help woud be appreciated

    y' = tan(x)sec^2(x)
    Make the substitution z=\sec x

    y' = 3x^(-1/2)
    Use the simple power rule...

    --Chris
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    8
    aight these are the answers that i got

    y' = tan(x)sec^2(x) -> y = sec^2(x)tan(x)

    y' = 3x^(-1/2) -> y = 1/(2x^(3/2))

    y' = -2cot^2(x)csc(x) -> y = 2 (ln(abs(sin(x))))(csc(x))

    did i get it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2008
    Posts
    8
    pls help me out guys
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Take the derivative of your answer and if it matches your integral than it is right.

    The answer for the 1st is

    \frac{\sec^2{x}}{2} + c
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2008
    Posts
    8
    can u show me the steps on how u got that answer please?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by sess View Post
    can u show me the steps on how u got that answer please?
    \int \tan{x}\sec^2{x}~dx

    Like chris said

    \sec{x}= u

    \sec{x}\tan{x}dx=du

    \int u^{n}~du = \frac{u^{n+1}}{n+1} + C

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

  8. #8
    Newbie
    Joined
    Sep 2008
    Posts
    8
    ok Ive no idea wat u just said

    i do know that the first derivative of sec(x) is sec(x)tan(x) right?

    i also know that the first derivative of tan(x) is sec^2(x)

    Where do i go from here? I really must appologize to you 11rdc11
    I have not understood the concept of finding the anti-derivative at all

    Would you please be so kind and explain?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by sess View Post
    ok Ive no idea wat u just said

    i do know that the first derivative of sec(x) is sec(x)tan(x) right?

    i also know that the first derivative of tan(x) is sec^2(x)

    Where do i go from here? I really must appologize to you 11rdc11
    I have not understood the concept of finding the anti-derivative at all

    Would you please be so kind and explain?
    Ok do you know the basic integral formula

    \int u^{n}~du = \frac{u^{n+1}}{n+1} + C
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Sep 2008
    Posts
    8
    Quote Originally Posted by 11rdc11 View Post
    Ok do you know the basic integral formula

    \int u^{n}~du = \frac{u^{n+1}}{n+1} + C
    yep i understand that part
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by sess View Post
    yep i understand that part
    Ok n just represents the power.

    So notice if we plug in the u of sub that I showed earlier the problem becomes the basic formula. Then just continue using the integral formula and back sub in the end.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. anti-derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 4th 2010, 06:15 PM
  2. Anti-Derivative using u and du.
    Posted in the Calculus Forum
    Replies: 10
    Last Post: July 19th 2009, 04:31 PM
  3. Anti-Derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: July 16th 2009, 05:30 PM
  4. Anti derivative
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 22nd 2008, 11:10 AM
  5. Anti-Derivative
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 31st 2008, 06:10 PM

Search Tags


/mathhelpforum @mathhelpforum