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Math Help - Calculus (2 problems)

  1. #1
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    Exclamation Calculus (2 problems)

    1) explain geometrically why the integral from 1 to 2 of x^2 dx equals the integral from 0 to 2 of x^2 dx minus the integral from 0 to 1 of x^2 dx and show that can be writen as the integral from 1 to 2 of x^2 dx = the integral from 1 to 0 of x^2 dx + the integral from 0 to 2 of x^2 dx

    AND...

    2) find a E (0, 2pi] such that the integral from 0 to a of sin x dx = 0

    THANKS FOR THE HELP!!!
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  2. #2
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    for the first one it would be helpful for you to draw the graph of x^2 and the see what areas you are calculating, hopefully it will become clearer to you.
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  3. #3
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    Quote Originally Posted by juicysharpie View Post
    [snip]
    2) find a E (0, 2pi] such that the integral from 0 to a of sin x dx = 0

    THANKS FOR THE HELP!!!
    You can either solve \int_0^a \sin x \, dx = 0 for a by first integrating and then solving the resulting trigonometric equation.

    Or you can draw a graph of y = \sin x starting at (0, 0) and ending at (2 pi, 0) and examine it to see what value of x gives a graph with the same area above the x-axis as below (use symmetry). That value of x will be the value of a you require.
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    Question

    does anyone else have any ideas that would better explain how to solve those two problems?
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  5. #5
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    Quote Originally Posted by juicysharpie View Post
    does anyone else have any ideas that would better explain how to solve those two problems?
    Maybe you should say what you don't understand about the replies you've been given. And perhaps the replies might make a bit more sense if you actually think about them for more than just a few minutes ....
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  6. #6
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    Question

    I don't understand how to find the integrate. I'm suppose to integrate and solve. How do I integrate to begin with?
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  7. #7
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    Well for the first question then you must draw a graph or explain one as it says "explain geonmetricly" therefore if you draw the graph then you can ask about what you dont understand
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  8. #8
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    Quote Originally Posted by juicysharpie View Post
    I don't understand how to find the integrate. I'm suppose to integrate and solve. How do I integrate to begin with?
    For Q2) it looks like you're expected to know what the integral of sin x is. Have you been taught that?

    http://www.ucl.ac.uk/Mathematics/geo...tnb/int2a.html

    Table of Integrals
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  9. #9
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    Quote Originally Posted by juicysharpie View Post
    does anyone else have any ideas that would better explain how to solve those two problems?
    Quote Originally Posted by Mr Fantastic View Post
    Maybe you should say what you don't understand about the replies you've been given. And perhaps the replies might make a bit more sense if you actually think about them for more than just a few minutes ....
    I didn't mean any harm. I just don't understand the problems and is just looking for some help, some answers/explanations that would clarify the problems to me. Again, I apologize and my reply was not meant to be offensive.
    Last edited by mr fantastic; January 18th 2009 at 04:24 AM. Reason: Removed reference to the infraction and added the quotes.
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