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Math Help - A few integrals..

  1. #1
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    A few integrals..

    A few integrals..-prob1.pngA few integrals..-prob2.png
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Bracketology View Post
    Click image for larger version. 

Name:	prob1.png 
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ID:	19208Click image for larger version. 

Name:	prob2.png 
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    This looks like it is for some kind of online homework...
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  3. #3
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    Yea...2 questions out of the 50 I have to do, Can you give me a place to start?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Bracketology View Post
    Yea...2 questions out of the 50 I have to do, Can you give me a place to start?
    Sure, the area, \displaystyle A between two curves \displaystyle f(x) and \displaystyle g(x) on an interval [a,b] is given by \displaystyle A = \int_a^b [f(x) - g(x)]~dx

    provided \displaystyle f(x) is always the top function on the interval \displaystyle [a,b]
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  5. #5
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    Quote Originally Posted by Bracketology View Post
    Yea...2 questions out of the 50 I have to do, Can you give me a place to start?
    You can use symmetry here and Jhevon's hint then

    \displaystyle \int_0^a (c^2-x^2)-(x^2-c^2) ~dx = 65

    where 'a' is the solution to \displaystyle  c^2-x^2=x^2-c^2\implies x = \frac{c}{\sqrt{2}}
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  6. #6
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    Thanks. I really appreciate it. I worked on this problem a good 20 minutes. and Somehow the c's kept canelling out.
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Bracketology View Post
    Thanks. I really appreciate it. I worked on this problem a good 20 minutes. and Somehow the c's kept canelling out.
    How do the c's cancel out?
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