Results 1 to 4 of 4

Math Help - Evaluating Integrals

  1. #1
    Junior Member
    Joined
    Mar 2007
    Posts
    56

    Evaluating Integrals

    Evaluate the following integral by interpeting it in terms of areas:

    The definite integral of f(x) from 1 to 0

    f(x) = sqrt(1 - x^2)dx = (1/4)3.14x^2 = (1/4)3.14(1)^2 = 3.14/4

    This is an example that was given in my text book. I don't undersatnd the second step (that part in bold type). Can someone please exlpain why the anti-derivative of sqrt(1 - x^2)dx is (1/4)3.14x^2?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member ecMathGeek's Avatar
    Joined
    Mar 2007
    Posts
    436
    Quote Originally Posted by zachb View Post
    Evaluate the following integral by interpeting it in terms of areas:

    The definite integral of f(x) from 1 to 0

    f(x) = sqrt(1 - x^2)dx = (1/4)3.14x^2 = (1/4)3.14(1)^2 = 3.14/4

    This is an example that was given in my text book. I don't undersatnd the second step (that part in bold type). Can someone please exlpain why the anti-derivative of sqrt(1 - x^2)dx is (1/4)3.14x^2?
    They cheated! But it works.

    Notice that f(x) = sqrt(1 - x^2) is the equation of the upper half of a circle with radius 1. Notice that if you integrate from x = 0 to x = 1, you are finding the area of (1/4) of the area of that circle. Let's cheat and do this the easy way:

    (1/4)*A(rea of a circle) = (1/4)*pi*r^2 = (1/4)*3.14*1 = 3.14/4
    Follow Math Help Forum on Facebook and Google+

  3. #3
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by zachb View Post
    Evaluate the following integral by interpeting it in terms of areas:

    The definite integral of f(x) from 1 to 0

    f(x) = sqrt(1 - x^2)dx = (1/4)3.14x^2 = (1/4)3.14(1)^2 = 3.14/4

    This is an example that was given in my text book. I don't undersatnd the second step (that part in bold type). Can someone please exlpain why the anti-derivative of sqrt(1 - x^2)dx is (1/4)3.14x^2?
    I got a different answer:

    EDIT: Ah, okay, ecMathGeek to the rescue! (Why do I have to think so complicated all the time?). I'll leave this up though, it might help somebody
    Attached Thumbnails Attached Thumbnails Evaluating Integrals-int.gif  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Here is another way. If you do not like it then do not use it.
    Attached Thumbnails Attached Thumbnails Evaluating Integrals-picture27.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Evaluating Integrals
    Posted in the Calculus Forum
    Replies: 6
    Last Post: June 7th 2011, 09:29 AM
  2. Evaluating integrals
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 14th 2010, 05:13 PM
  3. evaluating integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 10th 2009, 11:51 AM
  4. Evaluating integrals
    Posted in the Calculus Forum
    Replies: 9
    Last Post: February 4th 2009, 03:20 PM
  5. Evaluating Integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 14th 2008, 08:11 AM

Search Tags


/mathhelpforum @mathhelpforum