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P3 Question, I'm stumped. watch

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    Use the substitution t=tanx to show:

    ∫ 1/(3+5sin2x) dx = ∫ 1/(3t+1)(t+3) dt.

    Cheers.
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    Well if t = tanx, dt/(secx)^2 = dx, and 1 + t^2 = (secx)^2 so dx = dt/(1+t^2)
    ∫ 1/(3+5sin2x) dx = ∫ 1/(3+10sinxcosx) dx and sinx cosx = tanx(cosx)^2 = tanx/(secx)^2 = t/(1+t^2)
    So you have ∫ 1/(3+10sinxcosx) dx = ∫ 1/(3+10t/(1+t^2)) dt/(1+t^2)
    =∫ 1/(3+3t^2+10t) dt = ∫ 1/(3t+1)(t+3) dt
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    (Original post by Bhaal85)
    Use the substitution t=tanx to show:

    ∫ 1/(3+5sin2x) dx = ∫ 1/(3t+1)(t+3) dt.

    Cheers.
    INT 1/(3 + 5sin2x) dx

    = INT 1/(3 + 10sinx.cosx) dx

    = INT 1/(3 + 10tanx cos^2x) dx

    t = tanx => dt/dx = sec^2x = 1 + t^2

    INT 1/(3 + 10t(1/(1+t^2))) (1/(1 + t^2)) dt

    = INT 1/(3(1+t^2) + 10t) dt

    = INT 1/(3t^2 + 10t + 3) dt

    = INT 1/(3t + 1)(t + 3) dt

    Sorry if its hard to follow
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    Alternatively,
    1/(3t+1)(t+3) = 1/(3t^2 + 10t + 3)

    t = tan x
    dt/dx = sec^2,
    1/(3t^2 + 10t + 3) = sec^2/(3tan^2 + 10tan + 3) = 1/cos^2((3tan^2 + 10tan + 3)
    = 1/(3sin^2 + 10sincos + 3cos^2) = 1/(3+5sin2x)
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    (Original post by It'sPhil...)
    INT 1/(3 + 5sin2x) dx

    = INT 1/(3 + 10sinx.cosx) dx

    = INT 1/(3 + 10tanx cos^2x) dx

    t = tanx => dt/dx = sec^2x = 1 + t^2

    INT 1/(3 + 10t(1/(1+t^2))) (1/(1 + t^2)) dt

    = INT 1/(3(1+t^2) + 10t) dt

    = INT 1/(3t^2 + 10t + 3) dt

    = INT 1/(3t + 1)(t + 3) dt

    Sorry if its hard to follow
    10sinx.cosx = 10tanx cos^2x How?
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    (Original post by Bhaal85)
    10sinx.cosx = 10tanx cos^2x How?
    10sinx.cosx = 10sinx.cosx (cosx/cosx)

    = 10sinx/cosx (cosx)(cosx)
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    (Original post by It'sPhil...)
    10sinx.cosx = 10sinx.cosx (cosx/cosx)

    = 10sinx/cosx (cosx)(cosx)
    Is that from the dx/dy part?
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    (Original post by Bhaal85)
    Is that from the dx/dy part?
    I haven't done anything to it ive just timesed it by 1 in a helpful form ie 1 = cosx/cosx. Then i have grouped the terms differently
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    Am I correct in assuming that this is quite a testing question?

    Cheers people.
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    (Original post by Bhaal85)
    Am I correct in assuming that this is quite a testing question?

    Cheers people.
    Yes, this would not turn up on a P3 exam; it would more likely be on P5.
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    (Original post by mikesgt2)
    Yes, this would not turn up on a P3 exam; it would more likely be on P5.
    Excellent, I managed to do this by myself(yay me) the other day whilst powering through the review exercise..
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    (Original post by mikesgt2)
    Yes, this would not turn up on a P3 exam; it would more likely be on P5.
    similar question was on one of the past papers i got form my teacher.
 
 
 
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