Integration C4 Question

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  1. Jasmine_777's Avatar
    1 15-04-2012  00:10
    • Adored and Respected Member
    • Posts: 433
    Integration C4 Question
    Just came across a question where it says to integrate:

    1/sec^2y

    I thought you'd do 1/(1+tan^2x) but that seems to complicate matters ?

    Would appreciate the help,

    Many thanks!
  2. 0range's Avatar
    2 15-04-2012  00:15
    • Exalted and Worshipped Member
    Re: Integration C4 Question
    1/sec2y = cos2y

    this might help or I might be completely wrong xD
    I'm 80% sure this will will help though

    oh its a sqaured!
    yh intergrate cos^2y
    Last edited by 0range; 15-04-2012 at 00:17.
  3. raheem94's Avatar
    3 15-04-2012  00:16
    • TSR Demigod
    • Posts: 5,512
    Re: Integration C4 Question
    (Original post by Jasmine_777)
    Just came across a question where it says to integrate:

    1/sec^2y

    I thought you'd do 1/(1+tan^2x) but that seems to complicate matters ?

    Would appreciate the help,

    Many thanks!
    \displaystyle \int \frac1{sec^2y} \ dy

    We know \displaystyle sec^2y = \frac1{cos^2y}

    So the integral becomes, \displaystyle \int \frac1{sec^2y} \ dy = \int cos^2y \ dy

    Now use the identity, \displaystyle cos2y=2cos^2y-1
  4. Jasmine_777's Avatar
    4 15-04-2012  00:21
    • Adored and Respected Member
    • Posts: 433
    Re: Integration C4 Question
    (Original post by raheem94)
    \displaystyle \int \frac1{sec^2y} \ dy

    We know \displaystyle sec^2y = \frac1{cos^2y}

    So the integral becomes, \displaystyle \int \frac1{sec^2y} \ dy = \int cos^2y \ dy

    Now use the identity, \displaystyle cos2y=2cos^2y-1
    ooh doh! didn't see that.

    Thanks again!
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