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c4 integration help

( 1 + sin x ) ^2 dx
Reply 1
Avatar for Notnek
Notnek
21
Original post by IShouldBeRevising_
( 1 + sin x ) ^2 dx

Expand and integrate term by term.

For sin⁡2x\sin^2 x use the sine double angle formula.
Expand the bracket.

There is a standard method you should use to integrate sin⁡2x\sin^2 x with respect to x. Trawl back through your notes. It is very important and involves a trigonometric identity.
Original post by Mr M
Expand the bracket.

There is a standard method you should use to integrate sin⁡2x\sin^2 x with respect to x. Trawl back through your notes. It is very important and involves a trigonometric identity.


Do you get

X - 2COSX + 1/4(2x - sin2x)
(edited 11 years ago)
Reply 4
Avatar for joostan
joostan
13
Original post by IShouldBeRevising_
Do you get

X - 2COSX + 1/4(2x - sin2x)


Not quite there's a constant of integration missing, and its good practice to collect like terms.
Also

Spoiler

Original post by joostan
Not quite there's a constant of integration missing, and its good practice to collect like terms.
Also

Spoiler



What about

x - 2cosx + 1/4(2x - sin2x) + c
Reply 6
Avatar for joostan
joostan
13
Original post by IShouldBeRevising_
What about

x - 2cosx + 1/4(2x - sin2x) + c


Correct, though like I said, collecting like terms is good practice.
Original post by joostan
Correct, though like I said, collecting like terms is good practice.


What would the answer be if you collected like terms?
Reply 8
Avatar for joostan
joostan
13
Original post by IShouldBeRevising_
What would the answer be if you collected like terms?


3/2x - 2cos(x) - sin(2x)/4 +c
Or if you like:
1/4(6x - 8cos(x) - sin(2x)) +c
Original post by joostan
3/2x - 2cos(x) - sin(2x)/4 +c
Or if you like:
1/4(6x - 8cos(x) - sin(2x)) +c


Ok thanks for your help I cant seem to get the correct answer the question has the limits pi/4 and 0

I have subbed these in to the answer and im getting completely the wrong answer :frown:
Reply 10
Avatar for joostan
joostan
13
Original post by IShouldBeRevising_
Ok thanks for your help I cant seem to get the correct answer the question has the limits pi/4 and 0

I have subbed these in to the answer and im getting completely the wrong answer :frown:


What did you get?
Original post by joostan
What did you get?


A decimal
Reply 12
Avatar for joostan
joostan
13
Original post by IShouldBeRevising_
A decimal


1.513883683?
This is integral can be evaluated exactly. . .
Original post by joostan
1.513883683?
This is integral can be evaluated exactly. . .


Yeah thanks the answer is in exact form.
Reply 14
Avatar for joostan
joostan
13
Original post by IShouldBeRevising_
Yeah thanks the answer is in exact form.


Do you know the values for cos(0), sin(0), cos(pi/4) and sin(pi/2)?

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