Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

That one i can't get it

  1. Jan 8, 2004 #1
    hi, i'm sorry i'm asking alot, but that time i need help

    here the question says:
    * Verify the inequality without evaluating the definite integrals:

    (integration [x^2] from 0 to 1) >= (integration [x^3] from 0 to 1)

    i can't solve that question without evaluating the integral
    so how can i start it???

    thank u alot ...and any efforts will be appreciated

    N.B. if anyone please could inform me how to write mathematical equations in a better form.
    Last edited: Jan 8, 2004
  2. jcsd
  3. Jan 8, 2004 #2


    User Avatar
    Science Advisor

    I'll give you a hint. Can you show that for all points on the interval x^2>=x^3?

  4. Jan 8, 2004 #3

    take the dy/dx of both sides.
  5. Jan 8, 2004 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Here's how you would write the equation:

    \int_0^1 x^2 \, dx \geq \int_0^1 x^3 \, dx

    (click the image to see the source code)
  6. Jan 9, 2004 #5
    You draw the graphs for x^2 & x^3
    In the interval [0,1]
    The area under the graph for x^2 is greater than x^3

    [tex]\Rightarrow\int_0^1 x^2 \, dx \geq \int_0^1 x^3 \, dx[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook