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    what substitution should i use if any? to integrate
    \displaystyle\int (1-0.01x^2)^4\ dx
    or is there another way?(i thought expanding it wouldd take too long)
    this is just part of a question in M4 which is stopping me from finishing the question
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    (Original post by physics4ever)
    what substitution should i use if any? to integrate
    \displaystyle\int (1-0.01x^2)^4\ dx
    or is there another way?
    this is just part of a question in M4 which is stopping me from finishing the question
    Just use the bit inside the bracket ie \displaystyle 1 - \frac{x^{2}}{100} = u
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    (Original post by JosephML)
    Just use the bit inside the bracket ie \displaystyle 1 - \frac{x^{2}}{100} = u
    i did that earlier and i got

    \displaystyle \int \dfrac{-5u^4}{(1-u)^{0.5}}\ du
    is that wrong?
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    (Original post by physics4ever)
    i did that earlier and i got

    \displaystyle \int \dfrac{-5u^4}{(1-u)^{0.5}}\ du
    is that wrong?
    To be honest, I've no idea and I'm lying in bed so I can't check. In an exam I would probably have just expanded because I'm lazy so maybe try that.

    You say you're doing an M4 question but you're evaluating an indefinite integral. What sort of question is it?
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    (Original post by JosephML)
    To be honest, I've no idea and I'm lying in bed so I can't check. In an exam I would probably have just expanded because I'm lazy so maybe try that.

    You say you're doing an M4 question but you're evaluating an indefinite integral. What sort of question is it?
    it is a definite integral,i just didnt put the limits on,too lazy :laugh:
    anyway i used dI/du=(dI/dx)(dx/du),I means the integrand
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    (Original post by physics4ever)
    it is a definite integral,i just didnt put the limits on,too lazy :laugh:
    anyway i used dI/du=(dI/dx)(dx/du),I means the integrand
    Ok, I can't say I understand your method but as long as it works then great . It does mean should probably start doing some more maths before uni as I'm clearly very rusty...
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    (Original post by JosephML)
    Ok, I can't say I understand your method but as long as it works then great . It does mean should probably start doing some more maths before uni as I'm clearly very rusty...
    what is your method?
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    (Original post by physics4ever)
    what substitution should i use if any? to integrate
    \displaystyle\int (1-0.01x^2)^4\ dx
    or is there another way?(i thought expanding it wouldd take too long)
    this is just part of a question in M4 which is stopping me from finishing the question
    I couldn't be bothered to write out the whole question, but to make it easier to expand I noticed that the bracket contains a DOTS, so I put u=1+0.1x which gives 1-0.1x=2-u and du=dx

    so you have  \int (u(2-u))^4 du = \int u^4 (2-u)(2-u)^3 du

    expanding the u^4 (2-u) allows you to split the integral up and you can use the binomial expansion for (1+h)^3 (which you probably know off thee top of your head) to expand this out.

    I am unsure as to the merit of this method, other than the fact that it avoids plugging the numbers into the formula for binomials to the power 4 and opts for the power of 3 instead which is easier to remember (for me at least). it also partially avoids the messy numbers.
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    (Original post by physics4ever)
    what is your method?
    Just expand \displaystyle (1-0.01x^{2})^{4} using pascal's triangle (1,4,6,4,1)
 
 
 
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