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anonymous

  • 5 years ago

help! definite integral: (2+cos^2theta/cos^2theta)dtheta when dtheta is from pi/4 to 0

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  1. anonymous
    • 5 years ago
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    break it to 2 integrals: int(2/cox thera) + int(cox^2(theta))/conx^2)= 2int(1/cox^2) + int(theta) d... finish it - let me know if there is a problem

  2. anonymous
    • 5 years ago
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    oups...cox=cos... typo

  3. amistre64
    • 5 years ago
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    \[\int\limits_{0}^{\pi/4} \frac{2+\cos^2(t)}{\cos^2(t)}dt\]

  4. amistre64
    • 5 years ago
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    split it up; like inik states...but with out the typo :)

  5. amistre64
    • 5 years ago
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    and we get: [S] 2sec^2(t) + 1 dt

  6. anonymous
    • 5 years ago
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    cool! :)

  7. amistre64
    • 5 years ago
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    we see that sec^2(t) is the sderivative of tan(t); and 1 is the derivative of t

  8. amistre64
    • 5 years ago
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    \[F(t) = 2\tan(t) + t ; [0,\pi/4]\]

  9. amistre64
    • 5 years ago
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    tan(0) = 0...so the 0 part is useless.... go with the pi/4

  10. amistre64
    • 5 years ago
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    2(1) + pi/4 = 2 + pi/4

  11. amistre64
    • 5 years ago
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    11.14159 -------- :) 4

  12. amistre64
    • 5 years ago
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    2.785...

  13. anonymous
    • 5 years ago
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    thank you so much this helped a lot i also had a question about the definite integral: ((1-(sqrtx))/sqrtx dx when dx=9 to 4 i got the answer -3 but am not sure on that. if you could help that would be awesome

  14. anonymous
    • 5 years ago
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    woops *4 to 9

  15. amistre64
    • 5 years ago
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    this is a plit as well; [S] 1/sqrt(x) - 1 dx ; turn that sqrt into an exponent to deal with it easier.. [S] x^(-1/2) - 1 dx ; becomes 2sqrt(x) - x ; [4,9]

  16. amistre64
    • 5 years ago
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    2(3) - 9 - [2(2)-4] 6 - 9 - (4-4) = -3

  17. anonymous
    • 5 years ago
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    perfect! just had to check

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