Maths c4 a level integration question

I was doing a past paper and came across integrating: (1-2cosx)^2
Why is it incorrect to use the reverse chain rule method?
Instead, the correct answer is found when you expand it and solve it

Reply 1

Laurenk18

Original post by student277

I was doing a past paper and came across integrating: (1-2cosx)^2
Why is it incorrect to use the reverse chain rule method?
Instead, the correct answer is found when you expand it and solve it

What exam board are you doing?

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Reply 2

Zacken

Original post by student277

I was doing a past paper and came across integrating: (1-2cosx)^2
Why is it incorrect to use the reverse chain rule method?
Instead, the correct answer is found when you expand it and solve it

The reverse chain rule only applies to functions of the form

(ax+b)^n

by their linearity. Alternatively, it applies to integrands of the form [texf]f'(x)f(x)^n which your one isn't.

Reply 3

oShahpo

Reverse chain rule only works for first degree polynomials. The reason is that if you integrate using reverse chain rule, you will get (trig function) raised to some power and divided by some the derivative of the trig function. Now try to take the derivative of this expression, you will find that the trig function you divided by has it's own derivative and makes the derivative different to the integrand you're dealing with.
Tl;dr: don't use reverse chain rule unless it's a first order polynomial, or when the derivative of the inside function is present outside the brackets (in the same term).

Reply 4

hellopls

because when you do that you have to introduce a new function of x which you cannot do. try differentiating back you won't get the same

Reply 5

student277

Original post by oShahpo

Thanks. So what you are saying is I should only use the reverse chain rule when x in the bracket has no power, and will not be able to do it with any trigs in a bracket?

Reply 6

student277

Original post by Laurenk18

What exam board are you doing?

Posted from TSR Mobile

edexcel

Reply 7

Zacken

Original post by student277

Thanks. So what you are saying is I should only use the reverse chain rule when x in the bracket has no power, and will not be able to do it with any trigs in a bracket?

DId you read my post? I said that it will work for functions of the form

(ax+b)^n

provided that

n \neq -1

Reply 8

student277

Original post by Zacken

DId you read my post? I said that it will work for functions of the form

(ax+b)^n

provided that

n \neq -1

oh okay, thanks. Also what about differentiating using the chain rule, would it sill not work?

Reply 9

oShahpo

Original post by student277

Thanks. So what you are saying is I should only use the reverse chain rule when x in the bracket has no power, and will not be able to do it with any trigs in a bracket?

When the x has no power (power of 1 to be more precise) OR when the brackets (any function) is multiplied by it's derivative :
(any function)*(the derivative of that function)