C4 Integration Quiz (tough stuff)

C4 Integration quiz

Can you integrate? You better had if you want to do well in C4.

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Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


7 comments on “C4 Integration Quiz (tough stuff)

  • A

    Good questions thanks

    Maybe better if you show the answer for the actual maths at the end.

    Just telling you but, isn’t the v=1 on the ln(x) question suppose to be v’=1? (2^x has one choice where it is v’=1)
    Also, there is 80% chance that “non of the above” is not at the bottom so shouldn’t it be non of the others?

    • Colin

      Thanks for the feedback — I’ve shied away from giving the answers to the integrals, mainly out of laziness.

      Thanks especially for the corrections, I’ve fixed them 🙂

  • mkami wambura

    where are questions?????

    • Colin

      They should show up after you click the big blue ‘Start’ button.

  • aayush ganesh

    Differentiating log base 2 is actually fairly straightforward.

    y = log2(x)

    2^y = x

    dx/dy = 2^y ln(2)

    dy/dx = 1/((2^y)ln(2))

    dy/dx = 1/xln(2)

    Imo, this is easier than writing 2^x in terms of e^x and following the e^x integration by recognition rules.

    The only reason it’s not used is because it’s not on the syllabus 🙁

    They put differentiating and integrating any exponential but not any logarithm. Doesn’t make much sense to me.

    • Colin

      I’d probably do it as:

      $y = \log_2(x) = \frac{\ln(x)}{\ln(2)}$

      $\dydx = \frac{1}{x} \times \frac{1}{\ln(2)}$ directly.

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