Methods in Calculus 4 • Integrating with Inverse Trig Functions • CP2 Ex3D • 🏆

Edexcel Core Pure Year 2

Fri 10/1/20

[calebcheung]

21:15 this is a quote I will always remember in my exams

[joeclayton]

Hi sir
If you use a trigonometric substitution such as x=sinu, and when you are changing the limits from limits in x to limits in u, why do we just use arcsin( of x value), why can’t we use any other u value except the one given by arcsin so for example if x limit is root 3/2 for x=sinu why do we just use pi/3 and not other solutions like 2pi/3 etc. for that limit.

[BBK]

at 7:27, a is a constant so shouldn't you just remove it because you're differentiating? is it if you differentiate or integrate in respect to one variable like dx/du, then you measure the rate of change of "u" compared to rate of change of "x" so where does the a play into this? what is "a" actually representing?

[idkidk]

Hi, I came across a question that asked the integral of 2e^x / (e^2x + 9) and the answer is 2/3 arctan (e^x / 3) . Could you please explain how this came about because to my understanding they used the integral of 1/x^2 + a^2 but the numerator is not 1 so is this even possible?

[mathboy]

Do note ex3d has an error in Q6 and 3d is in the wrong exercise as its hyperbolic. :)

[khanish]

For this chapter do we need to know the hyperbolic integrals?

[BBK]

at 1:16 when you say arcsin and arccos are the same, except the arccos has the negative in front. does that imply the graphs are just a -f(x) transformation of each other - a reflection in the x-axis? is this covered in another video (perhaps a further maths option module?) or does this have a name for seeing why this is?
also at 18:51 could you do that question with either arcsin or arccos, both?

[MohammadAwan-it]

Sir some of the questions in the exercises ask for like arctan(t) as t --> infinity. Apparently this evaluated to pi/2. How are we meant to deduce this sort of thing?? Many thanks

[BBK]

is there a logical way to remember the order you have to remember why it is "x = a tan u" and not "a = x tan u" or some other combination.

in another comment you mention "We look at the formula book to see what it integrates to, and use a related substitution - so if it integrates to arctanx, we use atanu. If it integrates to arcsinx, we use asinu, etc." but why is it in this order?

Someone else in the comments also said "you wouldn't be able to substitute it into the integral without complicated manipulation", what complex manipulation is meant by this?

[Tim]

Hi Sir, for this kind of integration why would you use the substition x=f(u) and not u=f(x) like usually we do integration by substitution?

[RB-jdyb]

for 3:10 how did you deduce the substitution you need to use was u = a sinx, u = a tan x i cant see how you came to that?

[ehehrrhr]

hi sir you know we have 1/arctan(x/a) how come arcsin doesn't have that 1/a in it too?