Results 1 to 3 of 3

Math Help - Integrals

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    55

    Post Integrals

    Can someone plz help me evaluate these integrals?

    integral(
    e^x(3 + e^x)^8 )dx


    integral(PI/6 PI/4) (sin(x)/(1+cos(x))^2)dx

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Feb 2010
    From
    Lisbon
    Posts
    51
    In both cases you can find a primitive quite quickly. Observe that

    \frac{d}{dx}(3+e^x)=e^x,

    so the chain rule yields, for a well-behaved function g:

    \frac{d}{dx}g(3+e^x)=e^xg'(3+e^x).

    In particular, choosing g(x)=x^9:

    \frac{d}{dx}(3+e^x)^9=9e^x(3+e^x)^8.

    Consequently

    \int e^x(3+e^x)^8\; dx=\frac{1}{9}(3+e^x)^9.

    Try applying the same method to the second one
    Follow Math Help Forum on Facebook and Google+

  3. #3
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by Sally_Math View Post
    Can someone plz help me evaluate these integrals?

    integral(
    e^x(3 + e^x)^8 )dx


    integral(PI/6 PI/4) (sin(x)/(1+cos(x))^2)dx

    \int ^{\pi/6}_{\pi/4} \left[ \frac{\sin (x)}{(1+\cos (x))^2}\right]

    Let u = 1+\cos(x)<br />
    du = -\sin(x) dx

    dx = -\frac{du}{\sin(x)}

    Change the limits using our substitution:

    u_2 = 1+\cos \left(\frac{\pi}{6}\right) = \frac{2+\sqrt3}{2}

    u_1 = 1+ \cos \left(\frac{\pi}{4}\right) = \frac{2+\sqrt2}{2}


    <br />
-\int ^{\frac{2+\sqrt3}{2}}_{\frac{2+\sqrt2}{2}} \left(\frac{du}{u^2}\right)

    Which should be easy enough to solve
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Contour Integrals (to Evaluate Real Integrals)
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 17th 2011, 09:23 PM
  2. integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 20th 2010, 01:54 PM
  3. Replies: 1
    Last Post: December 6th 2009, 07:43 PM
  4. Integrals and Indefinite Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 9th 2009, 04:52 PM
  5. Some integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 20th 2008, 01:41 AM

Search Tags


/mathhelpforum @mathhelpforum