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Math Help - The fundamental theorem of calculus?

  1. #1
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    The fundamental theorem of calculus?

    Evaluate the definite integral

    from x=1 to x=4

    ((x-2))/((square root x)) This is what I did

    x^(1/2)-(x)^(-1/2)

    (2/3)x^(3/2)-2x^(1/2)

    Did I set this up correctly?
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  2. #2
    Super Member Matt Westwood's Avatar
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    Re: The fundamental theorem of calculus?

    Looks okay to me.

    Whoops no, you're a factor of 2 out in the second term.
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  3. #3
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    Re: The fundamental theorem of calculus?

    What do you mean factor of 2 out in the second term?
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    Re: The fundamental theorem of calculus?

    hi homeylova223

    he means that you have lost the two from 2x^(-1/2)
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    Re: The fundamental theorem of calculus?

    So would I be left with

    (2/3)x^(3/2)-4x^(1/2) ?
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  6. #6
    Member anonimnystefy's Avatar
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    Re: The fundamental theorem of calculus?

    that is correct but don't forget the integration constant C.
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  7. #7
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    Re: The fundamental theorem of calculus?

    Quote Originally Posted by anonimnystefy View Post
    that is correct but don't forget the integration constant C.
    It's a definite integral, so the C isn't needed. Instead the OP needs to find the difference between the integral value when it is evaluated at the upper and lower terminals.
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  8. #8
    Member anonimnystefy's Avatar
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    Re: The fundamental theorem of calculus?

    hi Prove It

    sorry i didn't see that it was a definite integral.my mistake.
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