A-Level Maths: H5-24 Further Integration: Tricky Integration by Substitution Problems

[cg]

Hello Mr TLmaths, me and my maths class want to thank you for your hard work in your YouTube videos especially the playlist for year2 integration, they are very helpful and easy to understand. Thanks

[lilggs]

*Thank you, Especially for Showing the Questions you go through on the thumbnail*
I literally came specifically here because the question ∫8xsin(x^2),

I idiotically tried substituting both “8x” and “sinx”
And it was to the point I didn’t even bother trying to substitute “u = x² “ because I assumed it wouldn’t work - it just filtered to the back of my mind and even the fact that there was one more method to try was like a “forgotten, inaccessible memory”

So much so that I’d be willing to search the internet, for what could be a futile attempt that would end up wasting much more time.

Hate that my brain does this lol, happens a lot

[y.m.]

Out of curiosity, for Q3, how does an substitution of x=sin(u) work? It seems out of the blue

[karya]

Insanly helpful videos🙏you are a god sir

[shamsalih]

If like question 3 you have an x^2 at the bottom in front of the square root, what substitution do you recommend using and do you mind explaining how you came to choose that?

[x_nova_x]

sir how do you now when to change limits?

[amirbatayi]

For question 1 why didn’t you substitute x with U as well you’ve only changed the sin function is this for x being cancelled out later on should I be doing the same thing and keep x whenever it’s going to be cancelled. Thanks ☺️
P.S I mean the x at back of sin x^3

[floralsparkle]

if a substitution isn't given would using a different one than the ones used in this video still get to the same answer?

[alexboyle]

why don't you for question 2 sub the tanx back into e^u after integrating the function ? As we let u = tanx

[wqltr]

Unless I'm mistaken, sqrt(x^2) is not always x, but rather abs(x). So im just curious what the justification is for sqrt(cos^2(x)) = cosx.

[mohammedimran]

hi how do you get the arc at the end and ur videos are extremely usefull

[vilsenshima]

Do we always have to change the limits, because I kept is as square root of pi and 0 for the first question and still got the same answer ?

[atheneparton]

When you have a number with the du, how do you deal with it if nothing cancels it, eg du/2 . Would you bring 2 to before the integral sign?

[isaacwalker]

would you have to include plus or minus cos(u) when the square root is used in question 3?

[Ash-enul]

why did u not replace it with u at the end with 1/2 cos u why did you not replace u with x squared]

[JK-vmyo]

suprised u havent gone over the trig ones where u need to use double angle formula

[danielmoss]

Surely in an exam they won’t tell us what substitution to use? Am I wrong?