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anonymous

  • 5 years ago

solve integral (1-tan^2(x))

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  1. anonymous
    • 5 years ago
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    \[\int\limits_{?}^{?}1-\tan ^{2}x=\int\limits_{?}^{?}1-(\sec ^{2}x-1)\]

  2. Yuki
    • 5 years ago
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    1-tan^2(x) is a nice Identity... do you know what it is ?

  3. anonymous
    • 5 years ago
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    \[=\int\limits_{?}^{?}2-\sec ^{2}x\]

  4. anonymous
    • 5 years ago
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    2x-tanx+C

  5. Yuki
    • 5 years ago
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    just to let you know uzma, if you eliminate the _{}-{} part after "int" the limits of the integral will go away like this \[\int\limits\]

  6. anonymous
    • 5 years ago
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    oh thanks, i dint try it :)

  7. Yuki
    • 5 years ago
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    np :)

  8. anonymous
    • 5 years ago
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    \[\int\limits\]

  9. Yuki
    • 5 years ago
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    Lao, to remember the integrals of trig, you need to know the derivatives of them very well

  10. anonymous
    • 5 years ago
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    right ?:)

  11. Yuki
    • 5 years ago
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    for this one, d/dx(tan(x)) = sec^2(x) was the one tat uzma referred to

  12. Yuki
    • 5 years ago
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    @ uzma fantastic !

  13. anonymous
    • 5 years ago
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    thanks

  14. Yuki
    • 5 years ago
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    another one you will see a lot is things like \[\int\limits -\csc(x)\cot(x) dx\]

  15. Yuki
    • 5 years ago
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    if you try to do u-substitution or integration by parts, it will be a tough one, but if you remember d/dx csc(x) = -csc(x)cot(x) then we know that the integral that I showed you will have an ans csc(x) + C

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