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Integration of cos^3 x

By KK LEE

June 15, 2021

There are many methods to integrate $\sin^3 x$ .

1. Use trigonometric identity

Given that $\sin (3x)=3\sin x - 4 \sin^3 x$ , $\sin^3 x = \frac{1}{4} [3\sin x - \sin (3x)]$ –

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STPM 2015 MT Chapter 8 Booklet A Page 20 Problem 11 Question 14

KK LEE Booklet Solution

Given that $y=\sec^{-1}(e^x)$ , prove that $\frac{dy}{dx}=\frac{1}{\sqrt{e^{2x}-1}}$ .

2015 MT Chapter 8 Booklet A Page 20 Problem 11 Question 11

KK LEE Booklet Solution

Given that $y=(\sin^{-1}x)^2$ , show that $(1-x^2)\frac{d^2y}{dx^2}-x\frac{dy}{dx}-2=$ 0.

STPM 2013 Mathematics (T) and (M) Final Grade

STPM Reference

This is the collection of the final grade of the new STPM Mathematics (T) year 2013. The final grade of Mathematics (T) is based on the grade of Paper 1, Paper 2, Paper 3, and Paper 4(PBS). All the exam marks are hidden and it is hard for STPM students to determine...

2015 MT Chapter 8 Booklet A Page 20 Question 6

KK LEE Booklet Solution

Given that $y=\ln(1+x)-x+\frac{1}{2}x^2$ show that $\frac{dy}{dx}>=0$ for all values of $x>-1$ .

2015 MT Chapter 8 Booklet A Page 20 Question 10

KK LEE Booklet Solution

If $\sin y = 2 \sin x$ , show that (a) $(\frac{dy}{dx})^2=1+3\sec^2 y$ , (b) by differentiating (a) with respect to $x$ , show that $\frac{d^2y}{dx^2}=3\sec^2 y \tan y$ , and hence that $\cot y \frac{d^2y}{dx^2}-(\frac{dy}{dx})^2+1=$ $0$ .

2015 MT Chapter 8 Booklet A Page 20 Question 8

KK LEE Booklet Solution

Given $y=\ln(\sin px + \cos px)$ . Prove that $\frac{d^2y}{dx^2}+(\frac{dy}{dx})^2+p^2=0$ .

Tags: Integration math MT Term 2 STPM MT

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KK LEE

KK LEE has been a STPM Mathematics tuition teacher since June 2006, but his love of Maths dates back to at least 1999 when he was Form 4. KK LEE started teaching in 2006 at Pusat Tuisyen Kasturi. He was known as "LK" when he was teaching in PTK. After teaching STPM Mathematics for 8 years in PTK, he joined Ai Tuition Centre in 2014. Over the years he has taught Mathematics (T), Mathematics (S), Mathematics (M), Additional Mathematics.

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Integration of cos^3 x

By KK LEE

1. Use trigonometric identity

STPM 2015 MT Chapter 8 Booklet A Page 20 Problem 11 Question 14

2015 MT Chapter 8 Booklet A Page 20 Problem 11 Question 11

STPM 2013 Mathematics (T) and (M) Final Grade

2015 MT Chapter 8 Booklet A Page 20 Question 6

2015 MT Chapter 8 Booklet A Page 20 Question 10

2015 MT Chapter 8 Booklet A Page 20 Question 8

KK LEE

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