A-Level Maths: H5-06 Further Integration: Examples of Reversing the Chain Rule Part 3

[helenday]

Phew, once again this AA man of the Highway of Maths has helped me out when my brain broke down.

[rachaelkenyon]

Hi sir, on Q4 why is it -1/2 sin as opposed to 1/2sin where does the minus come from? 😀

[x_nova_x]

sir can you beleive i almost got an A in an intergration test but i was one mark away because i forcorgot to add + c to my answer :( therefore losing one mark

[h]

does it matter which trig function you take to differentiate? If i integrate by substitution, would selecting u in this case, would be the function with the high order of power?

Recogning the interior function is confusing with different types of situations like dividing, product? i know with dividing we take the u as the denominator, what does interior function exactly meant to mean? If you took the numerator as u, for integration, would you get a wrong answer?

[sasharozanov]

In Q3, why is there a 2 in front of cos2x (when differentiating sin2x)? don't know where I would be without your videos by the way -- they're great!!

[sughrashabir]

Hi sir
Do u have videos integrating with trig identies.
Eg. Integral of sin^2 6x dx

[rafathchowdury]

for question 2 why can we use reverse chain because the derivative of cos is not sin it's -sin?

[tofjackn]

Hi sir,
I integrated sin(x)cos(x) and using the chain rule and got -1/2cos^2(x) + c
I then used the trig identity sin(x)cos(x) = 1/2sin(2x) and integrated that and I got -cos(2x)/4 + c
But what i don't understand is how to simplify -cos(2x)/4 to -1/2cos^2(x)
i got to -2cos^2(x)-1/4 which i simplified to -1/2cos^2(x)-1/4+c
and then im not sure where to go from there

does the -1/4 become part of the +c and then you just dont write it down?