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Math Help - Simple integration problem

  1. #1
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    Simple integration problem

    When you multiply 2cos(t) by 2cos(t), do you get 4cos(t)^2 or 4cos^2(t)? And also, assuming I have decided to make the defined integral ((4cos(t)^2 + 25 + 4sin(t)^2))^1/2, do I solve this one by substitution? Because I don't see how. Maybe by completing the square? This is going back to college Calculus but I can't remember what it is exactly I should do to integrate this expression.


    Thanks for the help.
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  2. #2
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    4\sin^2t+4\cos^2t=4(\sin^2t+\cos^2t)=4

    So you need to compute

    \int\sqrt{29}\,dt

    Does that make sense?
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Undefdisfigure View Post
    When you multiply 2cos(t) by 2cos(t), do you get 4cos(t)^2 or 4cos^2(t)? And also, assuming I have decided to make the defined integral ((4cos(t)^2 + 25 + 4sin(t)^2))^1/2, do I solve this one by substitution? Because I don't see how. Maybe by completing the square? This is going back to college Calculus but I can't remember what it is exactly I should do to integrate this expression.


    Thanks for the help.
    Maybe it is simply that you aren't familiar with typing these, but
    cos^2(t) = cos(t)^2 = cos^2(t) = cos(t) \times cos(t)

    cos(t^2) = cos(t^2)

    -Dan
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  4. #4
    Senior Member polymerase's Avatar
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    Quote Originally Posted by Undefdisfigure View Post
    When you multiply 2cos(t) by 2cos(t), do you get 4cos(t)^2 or 4cos^2(t)? And also, assuming I have decided to make the defined integral ((4cos(t)^2 + 25 + 4sin(t)^2))^1/2, do I solve this one by substitution? Because I don't see how. Maybe by completing the square? This is going back to college Calculus but I can't remember what it is exactly I should do to integrate this expression.


    Thanks for the help.
    Use the identity: cos^2x + sin^2x = 1
    Therefore:

    <br />
\int \sqrt{4cos^2x + 4sin^2x +25}\,dx = \int \sqrt{4(cos^2x + sin^2x) +25}\,dx = \int \sqrt{4 +25}\,dx<br />

    <br />
\int \sqrt{29}\,dx = \sqrt{29}x + C\<br />
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