C4 integration worked eg q

Why can't they use y= tanx instead of sec^4x? How do we know?

If we used y = tan x, then dy/dx = sec^2 x, which is not what we are trying to integrate. The idea is to take a resonable first guess as to what the integral will come to (by which I mean it needs to be right bar a constant multiplier).

How do you know what our first guess should be? Experience. You have to have done a good amount of chain rule differentiation so that you can look at an integral like this and say "Ah, I see what the answer is going to look like, becasue I've used the chain rule to differentiate so often that I can recognise it". Any by this, I don't mean that you should recognise every single thing you need to integrate, but that you should recognise general patterns.

[Edited to correct a very silly differention mistake!]

(edited 5 years ago)

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