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integration question

swim2daendswim2daend Registered User Posts: 2,497 Senior Member
edited September 2007 in AP Tests Preparation
The question is:
Let f(x)=3 if x is less than or equal to 3 and 6-x if x is greater than 3. Use geometric formulas to finmd the integration from 0 to 5 f(x)dx.
Post edited by swim2daend on

Replies to: integration question

  • TheMathProfTheMathProf Registered User Posts: 810 Member
    I would sketch a graph of this particular function. Draw line segments from the x-axis up to f(x) = 3 at x = 0 and x = 3, and draw line segments from the x-axis up to f(x) = 6-x at x = 3 and x = 5.

    You should recognize the two shapes that are enclosed and can find the areas of those pieces.

    BTW, what text are you doing that you guys are doing integration at this time of the year?
  • It'sGr82BeAGatorIt'sGr82BeAGator Registered User Posts: 513 Member
    This one is just finding the area underneath the curve from x=0 to 5, which is easy to do since you have a rectangle and a triangle as the curve
  • swim2daendswim2daend Registered User Posts: 2,497 Senior Member
    We're not doing this yet in the year. I took calc 1 over the summer and had a really bad teacher and I was just going through my old notes and tests looking at questions i couldn't answer before. I'm taking AP Calc AB (my school won't allow me to move up even though I took calc 1 at a CC) and we use the same book I used over the summer.
  • sishu7sishu7 Registered User Posts: 567 Member
    Very easy - do the integral of 3 from 0 to 3 - which is 9.

    Then do the integral of 6-x from 3 to 5 = 6x-.5x^2 from 3 to 5 = 27.5 - 13.5 = 14.

    Add them up to get 14 + 9 = 23. :)
  • TheMathProfTheMathProf Registered User Posts: 810 Member
    sishu, the question asked for geometric formulas, which your integral of 6-x omits.
This discussion has been closed.