Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Integration from AEA

2)
a) Show that

\sin 3x \equiv 3\sin x - 4\sin^3x

(3 marks)
I have done this.

Hence find
b)

\int \cos x(6\sin x - 2\sin 3x)^{\frac{2}{3}} dx

(3 marks)
I have done this.

c)

\int (3\sin 2x - 2\sin 3x \cos x)^{\frac{1}{3}} dx

(4 marks)

I have simplified the integrand to

\int (8\sin^3x\cos x)^{\frac{1}{3}} dx

but I am unsure of how to proceed.

Original post by Quivai

2)
a) Show that

\sin 3x \equiv 3\sin x - 4\sin^3x

(3 marks)
I have done this.

Hence find
b)

\int \cos x(6\sin x - 2\sin 3x)^{\frac{2}{3}} dx

(3 marks)
I have done this.

c)

\int (3\sin 2x - 2\sin 3x \cos x)^{\frac{1}{3}} dx

(4 marks)

I have simplified the integrand to

\int (8\sin^3x\cos x)^{\frac{1}{3}} dx

but I am unsure of how to proceed.

(8\sin ^3x\cos x)^{\frac{1}{3}} \equiv 2(\cos x)^{\frac{1}{3}}\sin x

. Can you see an obvious substitution from this form of the integrand?
Hint:

\dfrac{d}{dx}[\cos x] = -\sin x

How do you do the first part? I have done it via De Moivre's theorem (FP2-Edexcel) but am unsure how to do it in a Core Maths way

Original post by Gome44

How do you do the first part? I have done it via De Moivre's theorem (FP2-Edexcel) but am unsure how to do it in a Core Maths way

You mean part 2a - working out sin(3x)?

That's just a straightforward application of the addition formula for sin(2x + x), with a conversion of cos2x into sin^2x thrown in as well :smile:

:smile:

Ok, cool.

I always over-complicate things

Quick Reply

Latest

Trending

Trending

Articles for you

Students react after A-level Maths Paper 3 on 20 June

Students react after A-level Maths Paper 3 on 20 June

What is an LLM and how could it benefit your career?

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Powerful questions business students forget to ask their career advisers

Why I chose a law degree and what studying law was like

Why I chose a law degree and what studying law was like