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Math Help - Evaluate the integral using the FTC I

  1. #1
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    Evaluate the integral using the FTC I

    t-1/square root of t dt

    the integral is from 1 to 27 or 27
    1
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Lisa30907 View Post
    t-1/square root of t dt

    the integral is from 1 to 27 or 27
    1
    Is it
    \int_1^{27}\frac{t-1}{\sqrt t}dt

    or

    \int_1^{27}t-\frac{1}{\sqrt t}dt??

    And what is FTC?
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  3. #3
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    THE FIRST ONE

    fundamental theorem of calculus
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  4. #4
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    Quote Originally Posted by Lisa30907 View Post
    THE FIRST ONE

    fundamental theorem of calculus
    \frac{t-1}{\sqrt{t}} = \frac{t}{\sqrt{t}} - \frac{1}{\sqrt{t}} = t^{\frac{1}{2}} - t^{-\frac{1}{2}}<br />

    \int_1^{27} t^{\frac{1}{2}} - t^{-\frac{1}{2}} \, dt

    can you proceed from this point?
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  5. #5
    Super Member malaygoel's Avatar
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    \frac{t}{\sqrt t}=\sqrt t

    and its anti-derivative is \frac{2}{3}t^{\frac{3}{2}}

    \frac{1}{\sqrt t}=t^{\frac{-1}{2}}

    and its anti-derivative is 2t^{\frac{1}{2}}

    Can you do now???
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  6. #6
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    im working on it
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