You are Here: Home >< A-levels

# C4 integration by substitution question

Announcements Posted on
Four hours left to win £100 of Amazon vouchers!! Don't miss out! Take our short survey to enter 24-10-2016
1. From Solomon C integrate 12piSin^2 2t Costt dt limites 0 and pi/2, using substitution u=sint.

I got 4 pi, but the markscheme got 32/5 pi, but i dont understand how they got there
2. *Bumb*
3. You are missing something really important in the question. You can substitute sin(t) but not sin(2t) with u.
4. (Original post by Flo199)
You are missing something really important in the question. You can substitute sin(t) but not sin(2t) with u.
Thank you, stupid mistake
5. (Original post by kf141998)
From Solomon C integrate 12piSin^2 2t Costt dt limites 0 and pi/2, using substitution u=sint.

I got 4 pi, but the markscheme got 32/5 pi, but i dont understand how they got there
New Limits:
t=0, u=0
t=Pi/2 , u=1

u=sintdu/dt=cost
Therefore 1/cost du =dt

12pisin^2(2t)cost dt =
(12pisin^2(2t)cost)/cost=
12pisin^2(2t)
12pi (sin2t)(sin2t)
12pi (2sintcost)(2sintcost)
48pi sin^2(t) cos^2 (t)
48pi sin^2 (t) (1-sin^2 (t))
48pi u^2 (1-u^2)=
48pi u^2 -48pi u^5

Integrate..... = 16pi u^3 - 48/5 u^6

Sub in u values
(u=1) - (u=0)= Just u=1=
80/5 pi -48/5 pi=
32/5 pi
Hope this helped
6. (Original post by 1ncompl)
New Limits:
t=0, u=0
t=Pi/2 , u=1

u=sintdu/dt=cost
Therefore 1/cost du =dt

12pisin^2(2t)cost dt =
(12pisin^2(2t)cost)/cost=
12pisin^2(2t)
12pi (sin2t)(sin2t)
12pi (2sintcost)(2sintcost)
48pi sin^2(t) cos^2 (t)
48pi sin^2 (t) (1-sin^2 (t))
48pi u^2 (1-u^2)=
48pi u^2 -48pi u^5

Integrate..... = 16pi u^3 - 48/5 u^6

Sub in u values
(u=1) - (u=0)= Just u=1=
80/5 pi -48/5 pi=
32/5 pi
Hope this helped
Thank you

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: June 8, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### Who is getting a uni offer this half term?

Find out which unis are hot off the mark here

Poll

## All the essentials

### Student life: what to expect

What it's really like going to uni

### Essay expert

Learn to write like a pro with our ultimate essay guide.

### Create a study plan

Get your head around what you need to do and when with the study planner tool.

### Resources by subject

Everything from mind maps to class notes.

### Study tips from A* students

Students who got top grades in their A-levels share their secrets