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

Just diving into integral calculus

  1. Jul 5, 2011 #1
    And the first thing I'm tackling is understanding the area of a shape by inscribed/circumscribed polygons.

    For example, the shape produced by the line: y = x + 1, the y axis, and the vertical line x = 2.

    Now, my understanding is that the area is the limit as n approaches infinity of the sum of the area of n inscribed rectangles.

    Can someone explain how this translates to actual math? How would I find the area of the above shape?
     
  2. jcsd
  3. Jul 5, 2011 #2

    Mark44

    Staff: Mentor

    Is the other boundary of your region the x axis? If that's the region, its shape is a trapezoid whose area is 4.

    Using the limit of a Riemann sum to get the value, you would divide the interval [0, 2] into some number of subintervals, and the use rectangles or some other shape to approximate the area above each subinterval.

    For example, if the interval is divided into 4 subintervals, and inscribed rectangles are used, the area estimate is found to be .5*1 + .5*1.5 + .5 * 2.0 + .5 * 2.5 = .5*(7) = 3.5.

    To get a better approximation, divide the interval into more subintervals.
     
  4. Jul 6, 2011 #3
    Is it a valid method for me to do F(2) - F(0) to arrive at that answer? Would I be applying the theorem correctly?

    [itex]F(x) = \frac{x^2}{2} + x[/itex]

    F(2) = 4
    F(0) = 0

    4-0 = 4

    Since we are bounded by x = 0 and x = 2?
     
  5. Jul 6, 2011 #4
    Yes.
     
  6. Jul 6, 2011 #5
    That's really powerful!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Just diving into integral calculus
  1. Integral Calculus (Replies: 27)

Loading...