You are Here: Home >< Maths

# Step 1992 Q 8. watch

1. We have already shown the following

Now, given that

I need to find f(x) and show that C= -2/15

So far, I've got

But now I'm stuck. Any hints on where I should be heading?
2. What STEP paper is it?
3. Je ne sais pas. II or III, I *think*
4. let p(t)=t^2f(t) then
int {0,x} f(t)dt=int{1,x} p(t)dt +x-x^5/5+C
int {0,x} f(t)dt=-int{x,1} p(t)dt +x-x^5/5+C
diff wrt to x
f(x)=-p(x)+1-x^4............................. ..using the first result on the 2 integrals.
i.e.
f(x)=-x^2f(x)+(1+x^2)(1-x^2)
(1+x^2)f(x)=(1+x^2)(1-x^2)
f(x)=1-x^2

putting back into the integrals

lhs integral=int {0,x} 1-t^2 dt
=x-x^3/3
rhs integral=int{1,x} t^2-t^4 dt
=[1/3-1/5]-[x^3/3-x^5/5]
=2/15-x^3/3+x^5/5
so lhs integral =rhs integral +x-x^5-2/15
5. by differentiating
we have

then

so

C=-2/15
6. Thank you very much

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:
Updated: October 19, 2006
Today on TSR

### University open days

• Southampton Solent University
Sun, 18 Nov '18
Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams