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Math Help - Integration Worksheet (Finding area under curve)

  1. #1
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    Integration Worksheet (Finding area under curve)

    I have a math packet due tomorrow and I really need a good grade on it. The problem is that I've been out of town all last week and I don't understand this at all! Below I've attached the link to a Google Document with pictures of each question; it looks long but there's only 8 problems and a bonus. I would appreciate ANY and ALL help, including an explanation of how to do it, showing actual work, or even just a helpful site. You can edit on the Google Doc as well. Please and thank you! As I said, I'm desperate!!!!!!

    https://docs.google.com/document/d/1...thkey=CISfm_MM
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  2. #2
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    Integration is often called antidifferentiation. It is equivalent to creating an infinite number of infinitely small rectangles that reach from the x-axis to the curve and approximating the sum of their areas. While you can find a proof of the rectangles with the "I'm Feeling Lucky Button" on google I'll quickly cover integrals.

    There are two main types of integrals Indefinite and Definite:

    Indefinite: These integrals are used to find the antiderivative of a function.
    - As I'm sure you know, the derivative of x^2 is 2x. Therefore, the antiderivative of 2x is x^2 + C. Why the + C at the end? Because the derivative of x^2 plus any constant would be 2x as the derivative of a constant is zero. The big C represent a "constant".

    Definite integrals: These integrals are used for finding a value for an area under a curve.
    Following Part 1 of the Fundamental Theorem of Calculus :

    The definite integral of f(x) from a lower limit of integration a to an upper limit of integration b is equivalent to F(b) - F(a) where F(x) is the antiderivative of f(x).
    So how on earth is that useful? When finding the area under a curve from x = a to x = b all we need to do is find the definite integral of the function ( f(x) ) from lower limit a to upper limit b. I hope this can get you started.

    This website should be able to help you as well. Integrals -- from Wolfram MathWorld

    Have a good one. Good luck.
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