Results 1 to 4 of 4

Math Help - Please Help me With Calculus: Integrals! Problems and 1 Derivative Problem w/ Pic!

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    8

    Exclamation Please Help me With Calculus: Integrals! Problems and 1 Derivative Problem w/ Pic!

    Hello to my lovely fellow math help forum posters,

    I am in need of help with the following problems involving evaluating integrals. I took a picture of the problems that I need help with. It's 3 integral problems and 1 derivative problem involving max/min etc.



    I would appreciate any help that can be given!!! I need help on the steps to this method.. step by step. Can someone write the steps out and take a picture of it and post it up because its easier than writing *int* instead of the integral sign?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member autumn's Avatar
    Joined
    Mar 2010
    From
    unfortunalty, im stuck in hicks state. IN.
    Posts
    41
    In (a) let  u=\cos x, so du=-\sin x dx you do the rest.

    For (b) let  u=1+\ln x, so du=x^{-1}dx

    For (c) just do parts twice.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,969
    Thanks
    1009
    Quote Originally Posted by nuvydeep View Post
    Hello to my lovely fellow math help forum posters,

    I am in need of help with the following problems involving evaluating integrals. I took a picture of the problems that I need help with. It's 3 integral problems and 1 derivative problem involving max/min etc.



    I would appreciate any help that can be given!!! I need help on the steps to this method.. step by step. Can someone write the steps out and take a picture of it and post it up because its easier than writing *int* instead of the integral sign?

    Thanks
    We're not here to do your homework for you...

    Just a few hints:

    6. a) Make the substitution u = \cos{x}.

    6. b) Make the substitution u = \ln{x} + 1.

    6. c) You will need to use integration by parts twice.

    7. a) The function is increasing when the derivative is positive, and decreasing when the derivative is negative.

    7. b) The function is concave up when the derivative is increasing, i.e. when the second derivative is positive, and concave down when the derivative is decreasing, i.e. where the second derivative is negative. There are inflection points where it changes from being concave up to concave down, i.e. where the second derivative is 0 or does not exist.


    In future, please show what work you have done and exactly where you need help.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Quote Originally Posted by nuvydeep View Post
    Hello to my lovely fellow math help forum posters,

    I am in need of help with the following problems involving evaluating integrals. I took a picture of the problems that I need help with. It's 3 integral problems and 1 derivative problem involving max/min etc.



    I would appreciate any help that can be given!!! I need help on the steps to this method.. step by step. Can someone write the steps out and take a picture of it and post it up because its easier than writing *int* instead of the integral sign?

    Thanks

    Hint:

    (1) For 1st integral: \int f'(x)f^2(x)\,dx=\frac{f^3(x)}{3}+C\,,\,\,f(x) any derivable function

    (2) For 2nd integral: if \int f(x)\,dx=F(x)\,,\,\,then\,\,\,\int g'(x)f(g(x))\,dx=F(g(x)) , with g(x) a derivable function ( note that here F(x) is the primitive function of f(x) )

    (3) For 3rd integral: do integration by parts with u=x^2\Longrightarrow u'=2x\,,\,\,v'=e^{-x}\Longrightarrow v=-e^{-x}

    (4) for 4th problem: a twice derivable function f(x) has:

    (i) a maximum point at (x_0,f(x_0)) if f'(x_0)=0\,,\,\,f''(x_0)<0

    (ii) a minimum point at (x_0,f(x_0)) if f'(x_0)=0\,,\,\,f''(x_0)>0

    The function is increasing when f'(x)>0 and decreasing when f'(x)<0 , and concave upwards when f''(x)>0 and concave downwards when f''(x)<0 .

    The function has an inflection point when the second derivative has different signs on the left and on the right of that point.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A few basic calculus derivative problems
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 3rd 2010, 02:34 PM
  2. Replies: 3
    Last Post: March 6th 2009, 07:53 AM
  3. Replies: 6
    Last Post: January 14th 2009, 07:28 PM
  4. calculus derivative problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 19th 2008, 06:46 PM
  5. Calculus Derivative problems
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 11th 2008, 04:45 PM

Search Tags


/mathhelpforum @mathhelpforum