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Math Help - trigonometric substitution

  1. #1
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    trigonometric substitution

     \int\ dx /\sqrt(25+x^2)\\ on the interval (0,1). So I use x=5tany, and dx=5sec^2y...
    I got it down to integral 5sec^2y / \sqrt(25(1+tan^2y)\
    and then substituting sec^2 for y=tan^2y...left me with 5sec^2y/5sec^2y..so Im left with the integral of 1, right?

    Then I get y+C....but how do I solve for y...I'm really confused, did I do all the above steps the right way?
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  2. #2
    Super Member TheChaz's Avatar
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    x = 5tan(y) -->
    x/5 = tan(y) -->
    arctan(x/5) = y
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  3. #3
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    thank you so much, I get it! how did I not see that...
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  4. #4
    Super Member TheChaz's Avatar
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    Calculus makes people do funny things! I've had students forget which quadrants are which, that the product of two negatives is postive, etc...
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