Results 1 to 3 of 3

Math Help - Help with an integral

  1. #1
    Junior Member xterminal01's Avatar
    Joined
    Nov 2007
    Posts
    52

    Help with an integral

    <br />
\int sin^2(x) cos^3(x) dx<br /> <br />
    My answer came out to be?
    <br /> <br />
sin^5x/5 - sin^3x/3<br />
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2009
    Posts
    202

    correct!

    Quote Originally Posted by xterminal01 View Post
    <br />
\int sin^2(x) cos^3(x) dx<br /> <br />
    My answer came out to be?
    <br /> <br />
sin^5x/5 - sin^3x/3<br />
    your answer seems to be correct. there will be 2 sins one with power 4 and the other with power 2 and a cos which will go with the dx once you get dt if t=sinx.but u must not forget the constant c!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,544
    Thanks
    1394
    Quote Originally Posted by xterminal01 View Post
    <br />
\int sin^2(x) cos^3(x) dx<br /> <br />
    My answer came out to be?
    <br /> <br />
sin^5x/5 - sin^3x/3<br />
    Write the integral as \int sin^2(x) cos^2(x) cos(x)dx= \int sin^2(x)(1- sin^2(x)) cos(x)dx = \int (sin^2(x)- sin^4(x)) cos(x)dx

    Now let u= sin(x) so that du= cos(x)dx and the integral becomes \int (u^2- u^4)du \frac{u^3}{3}- \frac{u^5}{5}+ C= \frac{sin^3(x)}{3}- \frac{sin^5(x)}{5}, the negative of your answer.

    It is always better, in asking for a check, to show your work.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 31st 2010, 07:38 AM
  2. Replies: 1
    Last Post: June 2nd 2010, 02:25 AM
  3. Replies: 0
    Last Post: May 9th 2010, 01:52 PM
  4. [SOLVED] Line integral, Cauchy's integral formula
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 15th 2009, 01:28 PM
  5. Replies: 0
    Last Post: September 10th 2008, 07:53 PM

Search Tags


/mathhelpforum @mathhelpforum