# C1- Integration help!

Watch
Announcements
#1
Can someone help me with the following two questions please

and that when , find the value of when

Right so the question comes under the topic of integration but I don't really understand what its asking me. If I was doing this in the exam I wouldn't know that I would have to integrate. So once I have integrated this. I got

What do I do next?

Next one is and the when , find the value of when . I think if I knew how to do the first question I should be able to do the second one. Any help would be appreciated. Thanks P.S how would I know that I would have to integrate this?
0
7 years ago
#2
when you integrate you must include a constant c
0
7 years ago
#3
You need to recognise the question gives you dx/dt which is the the differential with respect to t of y.
So you integrate dx/dt with respect to t and you should acquire t^3+t^2+t+k. You have t^3+t^2+x which shows you do not know what the actual process of integration is doing. Rewrite dx/dt if it make it more familiar to have say dy/dx. If you don't have limits to integrate between then you must assume there is some constant (k) which can be zero. Since x had been differentiated any constant will be lost in this process when integrating we must assume there was one there.

Posted from TSR Mobile
0
#4
(Original post by the bear)
when you integrate you must include a constant c
DAMN IT! I completely forgot
0
#5
(Original post by tmorrall)
You need to recognise the question gives you dx/dt which is the the differential with respect to t of y.
So you integrate dx/dt with respect to t and you should acquire t^3+t^2+t+k. You have t^3+t^2+x which shows you do not know what the actual process of integration is doing. Rewrite dx/dt if it make it more familiar to have say dy/dx. If you don't have limits to integrate between then you must assume there is some constant (k) which can be zero. Since x had been differentiated any constant will be lost in this process when integrating we must assume there was one there.

Posted from TSR Mobile
Right I understood that part, but what is it asking me to do when it gives values of x and t?
0
7 years ago
#6
(Original post by Super199)
Right I understood that part, but what is it asking me to do when it gives values of x and t?
So if you integrate dx/dt with respect to t you get the function of x so now you know x=t^3+t^2+t+k. You know a value for t when x is whatever. Sub them both in solve for your k so now you know the full equation since you know the constant k now. You can then do the next part. Note also that you have integrated with respect to t so the when you integrate the 1 it becomes t not x. If you had dy/dx is 10x+1 integrate with respect to x you get 5x^2+x+k not 5x^2+y+k

Posted from TSR Mobile
0
#7
(Original post by tmorrall)
So if you integrate dx/dt with respect to t you get the function of x so now you know x=t^3+t^2+t+k. You know a value for t when x is whatever. Sub them both in solve for your k so now you know the full equation since you know the constant k now. You can then do the next part. Note also that you have integrated with respect to t so the when you integrate the 1 it becomes t not x. If you had dy/dx is 10x+1 integrate with respect to x you get 5x^2+x+k not 5x^2+y+k

Posted from TSR Mobile
So if I sub 1 for t. What do I do about the x? Where would I sub x =2?
0
7 years ago
#8
(Original post by Super199)
So if I sub 1 for t. What do I do about the x? Where would I sub x =2?
You know that x=t^3-t^2+t+c at the point where t=1 AND x=2 so replace both your t and your x with their corresponding values and you get 2=1^3-1^2+1+c
2=1-1+1+c
c=1
So now you know the constant you have an equation which you know everything about: x=t^3-t^2+t+1

I hope I am not coming across too patronising. Trying to be as thorough as possible

Posted from TSR Mobile
0
#9
(Original post by tmorrall)
You know that x=t^3-t^2+t+c at the point where t=1 AND x=2 so replace both your t and your x with their corresponding values and you get 2=1^3-1^2+1+c
2=1-1+1+c
c=1
So now you know the constant you have an equation which you know everything about: x=t^3-t^2+t+1

I hope I am not coming across too patronising. Trying to be as thorough as possible

Posted from TSR Mobile
Oh wow you my friend are a lad!!!! I understand wow thanks. I got x = 7 as my answer . Thanks man!
0
7 years ago
#10
(Original post by Super199)
Oh wow you my friend are a lad!!!! I understand wow thanks. I got x = 7 as my answer . Thanks man!
Yeah thats it. The more you do calculus the greater your understanding will become. Arguably most applicable maths to real life this stuff!
Haha yeah no problem

Posted from TSR Mobile
0
#11
(Original post by majmuh24)
Integration is the inverse of differentiation, so if you have a derivative and want to find a function for x in terms of t, you have to integrate it with respect to t.

To find C, substitute the values that you have been given so x=2 and t=1, so just put these values into the equation you have from integrating the derivative.
Help me with this one please

a). Show that where A and B are constants to be found
B). Hench find the integral of ydx.

How do I start?
0
7 years ago
#12
(Original post by Super199)
Help me with this one please

a). Show that where A and B are constants to be found
B). Hench find the integral of ydx.

How do I start?
Well, what would you have to do to turn into
0
#13
(Original post by TenOfThem)
Well, what would you have to do to turn into
square it?
laws of indices. Then Where is the from?
0
7 years ago
#14
(Original post by Super199)
square it?
laws of indices. Then Where is the from?
Well what do you get when you expand ?
0
7 years ago
#15
(Original post by Super199)
square it?
laws of indices. Then Where is the from?
square the RHS too
1
#16
(Original post by davros)
Well what do you get when you expand ?
Right got it! Cheers
0
X

new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

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

### Poll

Join the discussion

#### How would you feel if uni students needed to be double vaccinated to start in Autumn?

I'd feel reassured about my own health (43)
14.83%
I'd feel reassured my learning may be less disrupted by isolations/lockdowns (95)
32.76%
I'd feel less anxious about being around large groups (36)
12.41%
I don't mind if others are vaccinated or not (24)
8.28%
I'm concerned it may disadvantage some students (17)
5.86%
I think it's an unfair expectation (72)
24.83%
Something else (tell us in the thread) (3)
1.03%