realicetic
Badges: 1
Rep:
?
#1
Report Thread starter 13 years ago
#1
hey
just having a bit of a blank,
how would you integrate

(cost)^4+(sint)^4
0
reply
Christophicus
Badges: 18
Rep:
?
#2
Report 13 years ago
#2
(Original post by realicetic)
hey
just having a bit of a blank,
how would you integrate

(cost)^4+(sint)^4
(cost)^4 + (sint)^4
= cos^4t + sin^4t
= cos^2t(cos^2t) + sin^2t(sin^2t)
= cos^2t(1-sin^2t) + sin^2t(1-cos^2t)
= cos^2t + sin^2t - 2sin^2t.cos^2t
= 1 - 2sin^2t.cos^2t
= 1 - 2sint.cost.sint.cost
= 1 - 0.5sin^2(2t)

cos4t= 1-2sin^2(2t)
=> sin^2(2t) = 0.5 - 0.5cos4t

1 - 0.5sin^2(2t)
= 1-0.5(0.5-0.5cos4t)
= 1-0.25+0.25cos4t
= 0.75+0.25cos4t
0
reply
Kolya
Badges: 15
#3
Report 13 years ago
#3
Just remember:

\huge cos2x = cos^2x - sin^2x = 2cos^2x -1 = 1 - 2sin^2x
0
reply
yazan_l
Badges: 5
Rep:
?
#4
Report 13 years ago
#4
(Original post by Widowmaker)

= 1 - 2sint.cost.sint.cost
= 1 - 0.5sin^2(4t)
u have a mistake here:
it's :

1 - 2sint.cost.sint.cost
= 1 - (sin2t . ½sin2t)
= 1 - ½sin²2t


Edit: hence u will get to 0.75+0.25cos4t which integrates to 0.75t+1/16 sin4t
0
reply
Christophicus
Badges: 18
Rep:
?
#5
Report 13 years ago
#5
(Original post by yazan_l)
u have a mistake here:
it's :

1 - 2sint.cost.sint.cost
= 1 - (sin2t . ½sin2t)
= 1 - ½sin²2t


Edit: hence u will get to 0.75+0.25cos4t which integrates to 0.75t+1/16 sin4t
arghh. I had that initially. Why did I change it?? :mad:
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • SOAS University of London
    Development Studies, Interdisciplinary Studies, Anthropology and Sociology, Languages, Cultures and Linguistics, Arts, Economics, Law, History, Religions and Philosophies, Politics and International Studies, Finance and Management, East Asian Languages & Cultures Postgraduate
    Sat, 25 Jan '20
  • University of Huddersfield
    Undergraduate Open Day Undergraduate
    Sat, 25 Jan '20
  • The University of Law
    Solicitor Series: Assessing Trainee Skills – LPC, GDL and MA Law - Guildford campus Postgraduate
    Wed, 29 Jan '20

Have you ever signed up for an open day and then not gone to it?

Yes (48)
48.48%
No (51)
51.52%

Watched Threads

View All