1. Limited time only! Sign up for a free 30min personal 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!

Find the integral of:

  1. Jul 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the integral of

    2. Relevant equations

    ∫(5x^2 + √x - 4/x^2 dx

    3. The attempt at a solution

    ∫(5x^2 + √x - 4/x^2 dx

    = 5 ∫x^2 dx + ∫√x dx ∫- 4/x^2
    = 5 [x^3/3] + ∫√x dx ∫- 4/x^2
    = 5 [x^3/3] + [x^1/2] dx ∫- 4/x^2
    = 5 [x^3/3] + [x^1/2] - [-4x^-2]
    = 5[x^3/3] + [x^1/2] + [4/x] + C
    = 5x^3/3 + x^1/2 + 4/x + C

    Does my final answer look right for this? I'm really struggling with integrals, and am hoping I'm getting to grip with it now, but if someone can verify that would be great.

    Thanks so much,

    Lloyd
     
  2. jcsd
  3. Jul 18, 2013 #2

    CAF123

    User Avatar
    Gold Member

    $$\sqrt{x} = x^{\frac{1}{2}},$$ You must then integrate this. The rest is fine.
     
  4. Jul 18, 2013 #3
    Thanks for fast reply.

    So do I add 1 to exponent = x^2/3
    Divide by same so = x^2/3 / 2/3

    From there can I simplify this to just x?

    Thanks

    Lloyd
     
  5. Jul 18, 2013 #4

    CAF123

    User Avatar
    Gold Member

    Yes, but 1/2 + 1 ≠ 2/3.

    Also xa/a ≠ x, for example x2/2 = 1/2 when x = 1.
     
  6. Jul 18, 2013 #5
    Really sorry I was being dumb there...

    I wrote in pen 3/2 then typed 2/3.

    So to recap:

    x^1/2
    Add 1 to exp' = X^3/2
    Divide by same = X^3/2 / 3/2

    From here there must be some simplification, as the fraction is improper?

    Or is that the conclusion?

    Thank you,

    Lloyd
     
  7. Jul 18, 2013 #6
    [itex]\int \sqrt{x} dx[/itex] = [itex]\int \ {x^{\frac{1}{2}}} dx [/itex]

    = [itex]\frac{2}{3} x^{\frac{3}{2}}[/itex]
     
  8. Jul 18, 2013 #7

    CAF123

    User Avatar
    Gold Member

    Yes, you can write $$\frac{x^{\frac{3}{2}}}{3/2} = x^{\frac{3}{2}} \frac{1}{3/2} = \frac{2}{3} x^{\frac{3}{2}}$$
     
  9. Jul 18, 2013 #8
    Thank you both.

    I'm still not 100% on these, but have come a long way (from knowing nothing to where I am now) in the last 7 hours.

    Thankfully calculus is only a mall proportion of the study I am doing.

    Thanks again,

    Lloyd
     
  10. Jul 18, 2013 #9
    All you need to do now is simplify :))

    [itex]\frac{5}{3}x ^{3} + \frac{2}{3} x^{\frac{3}{2}} + \frac{4}{x}[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Find the integral of:
  1. Find the integral. (Replies: 2)

  2. Find this integral (Replies: 12)

  3. Find this integration (Replies: 1)

  4. Find the integral? (Replies: 4)

  5. FInd this integral (Replies: 1)

Loading...