1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral help

  1. Mar 9, 2008 #1
    If you are told to evaluate the integral and are given this problem:

    ∫ (e√x / √x) dx

    This reads that the integral of (e) to the power of square root of x divided by the square root of x multiplied by the derivative of x is……

    I have tried solving it and came up with this, is this correct if not please show me what I did wrong and how I can solve it.

    y = x2 + 2

    y = sin x

    0 ≤ x ≤ π
    π π π π
    A(D) = ∫0 (x2 + 2 – sin x) dx = ∫0 x2dx + 2 ∫0 dx - ∫0 sin x dx =

    π π π
    [x 3 / 3 ]0 + 2[x]0 + [cos x]0 = π/3 + 2π – 2

    [cos x]0 = cos π – cos 0 = -1 – 1 = -2

    Is this correct?

    the integral goes from zero to pi. and x2 is x squared. Any help is appreciated.
  2. jcsd
  3. Mar 9, 2008 #2


    User Avatar
    Homework Helper

    [tex]\int \frac{e^{\sqrt{x}}}{\sqrt{x}} dx[/tex]

    Let [itex]t=\sqrt{x} \Rightarrow \frac{dt}{dx}=\frac{1}{2\sqrt{x}} \Rightarrow 2 dt=\frac{dx}{\sqrt{x}}[/itex]

    Can you take it from here?
    Last edited: Mar 9, 2008
  4. Mar 12, 2008 #3
    now do you turn the square root of x into the power of 1/2, then you raise it to the numerator it becomes -1/2, the direvative of that is 1/2 divided by one whic is one half. correct?
  5. Mar 12, 2008 #4
    No ... if you u-sub the sqrt of x in the numerator and take the derivative, a part of your integral will appear which lets you get rid of the one in the denominator.
  6. Mar 12, 2008 #5
    [tex]\int e^{\sqrt{x}}\frac{dx}{\sqrt x}[/tex]

    [tex]u=\sqrt x[/tex]
    [tex]du=\frac{dx}{2\sqrt x} \rightarrow 2du=\frac{dx}{\sqrt x}[/tex]

    Now make your substitutions ... hope this is a little more clear.

    [tex]2\int e^u du[/tex]
    Last edited: Mar 12, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integral help
  1. Integral help (Replies: 3)

  2. Help with an integral (Replies: 1)

  3. Help with integration (Replies: 3)

  4. Help with an integral (Replies: 3)

  5. Help with an integral (Replies: 0)