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Math Help - Upper and Lower bounds... Conceptual

  1. #1
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    Upper and Lower bounds... Conceptual

    Suppose we know that 1 \le \int_{0}^{4} g(x)dx \le 10. Determine the best possible upper and lower bounds for \int_{0}^{2} xg(x^2)dx that can be deduced from this information. Justify your answer.

    Again, I've no idea where to really start on this one... if someone could help me through it I'd appreciate it.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ebonyscythe View Post
    Suppose we know that 1 \le \int_{0}^{4} g(x)dx \le 10. Determine the best possible upper and lower bounds for \int_{0}^{2} xg(x^2)dx that can be deduced from this information. Justify your answer.

    Again, I've no idea where to really start on this one... if someone could help me through it I'd appreciate it.
    this is a substitution problem cleverly disguised. try the substitution u = x^2 (remember to change the limits also) and see what you get
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  3. #3
    Super Member angel.white's Avatar
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    Is it between .5 and 5?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by angel.white View Post
    Is it between .5 and 5?
    yes. inclusive, of course

    good job
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  5. #5
    Super Member angel.white's Avatar
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    Quote Originally Posted by Jhevon View Post
    yes. inclusive, of course

    good job
    Appreciate it, yesterday I didn't even know about changing the interval O.o

    It's amazing how I learn so much more from reading through questions on this site, than from studying my book.
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