Integration question

Integrate: 16sin^4(x)cos^4(x)

I think i can integrate it. But i dont know how to start/ how to simplify the sin^4(x)cos^4(x) into something simple which i can integrate. Any help appreciated!

(edited 9 years ago)

Reply 1

TeeEm

19

Original post by Nirm

Integrate: 16sin^4(x)cos^4(x)

I think i can integrate it. But i dont know how to start/ how to simplify the sin^4(x)cos^4(x) into something simple which i can integrate.

think of the identity for sin2A=2sinAcosA

Reply 2

Nirm

OP

13

Original post by TeeEm

think of the identity for sin2A=2sinAcosA

All i can think of is (sin2A)^4 but that doesnt seem right because the answer is meant to be 3x/8 - sin4x/8 +sin8x/64 (+C). I am going to give it a go and see if i get anywhere. Thanks for the hint :smile:

Reply 3

TeeEm

19

Original post by Nirm

All i can think of is (sin2A)^4 but that doesnt seem right because the answer is meant to be 3x/8 - sin4x/8 +sin8x/64 (+C). I am going to give it a go and see if i get anywhere. Thanks for the hint :smile:

next consider sin²A =1/2 - 1/2cos(2A)

Reply 4

TenOfThem

18

Original post by Nirm

All i can think of is (sin2A)^4 but that doesnt seem right because the answer is meant to be 3x/8 - sin4x/8 +sin8x/64 (+C). I am going to give it a go and see if i get anywhere. Thanks for the hint :smile:

Think you probably wanted to gothe other way and write your things in terms of cos2x instead