Integration question

anpanman SG

How do you integrate sin^2 x cos^2 x with the range of pi/2 and 0? Please show me step-by-step. I realised the questions in the textbooks don't have more than the power of 1. So yea, I can't solve this.

eagle SG

change the trigo this way

sin² x cos² x
= ¼ (4sin² x cos² x)
= ¼ (2 sin x cos x)(2 sin x cos x)
= ¼ sin² 2x ===> double angle formula
= ¼ (½ - ½ cos 4x)
= ⅛ - ⅛ cos 4x

You should be able to integrate this

wee_ws SG

Hi,

In the syllabus, the key integrals involving trigo are the integrals of:

1. sin² x,

2. cos² x,

3. tan² x.

For the integrals of sin^3 x and cos^3 x, the following results are useful:

cos 3x = 4cos^3 x - 3cos x,

sin 3x = 3sin x - 4 sin^3 x.

Thanks!

Cheers,
Wen Shih

dkcx SG

For the integrals of sin^3 x and cos^3 x, the following results are useful:

cos 3x = 4cos^3 x - 3cos x,

sin 3x = 3sin x - 4 sin^3 x.

Those are the things i hate most during sec sch and what cause me to fail my integration test on trigo :p

Forbiddensinner SG

Those are the things i hate most during sec sch and what cause me to fail my integration test on trigo :p

Using the formulaes is the easy part, proving them is what give me headache.

eagle SG

Hi,

In the syllabus, the key integrals involving trigo are the integrals of:

1. sin² x,

2. cos² x,

3. tan² x.

For the integrals of sin^3 x and cos^3 x, the following results are useful:

cos 3x = 4cos^3 x - 3cos x,

sin 3x = 3sin x - 4 sin^3 x.

Thanks!

Cheers,
Wen Shih

Add on:

one memonics to remember the cos 3x formula is to use hokkien for

$1.30 = $4.30 - $3
(kor san = si kor san minus san kor)

sin 3x will be opposite

Forbiddensinner, there are few rules to proving trigo identities that will make it much simpler... One obvious one would be always to start from the one looking most chim... then also change all to just sines and cosines (not always the case though, but mostly)

Other than that, for the new syllabus in A maths for double angle (and half angle) formulas, etc, one will need to try to match at least one trigo function to factorise (usually)...