OCR Core 3 integrating "e" question

Hi, I'm doing a 3 part question, and I've done the first two parts fine. This had led me to a (confirmed correct) question:

Show that between a and 0 the integral of (2 -e^(-x) -x)dx =1 +a -0.5a^2.

I did:

integrate the equation: [2x + e^-x -0.5x^2](a_0)

Sub in values of x: [2a + e^-a -0.5a^2]-[0+e^0 -0]

Which gave me: 2a + e^-a -0.5a^2 -1.

Clearly, this must have gone wrong at some point, since it barely even has any resemblance to 1 +a -0.5a^2. Could I possibly have some help?

(Apologies, I tried to use LaTeX, but it spat out a lot of code for colours and things I couldn't fix :frown:

)

(edited 9 years ago)

Reply 1

TeeEm

19

Original post by Azurefeline

Hi, I'm doing a 3 part question, and I've done the first two parts fine. This had led me to a (confirmed correct) question:

Show that between a and 0 the integral of (2 -e^(x) -x)dx =1 +a -0.5a^2.

I did:

integrate the equation: [2x + e^-x -0.5x^2](a_0)

Sub in values of x: [2a + e^-a -0.5a^2]-[0+e^0 -0]

Which gave me: 2a + e^-a -0.5a^2 -1.

Clearly, this must have gone wrong at some point, since it barely even has any resemblance to 1 +a -0.5a^2. Could I possibly have some help?

(Apologies, I tried to use LaTeX, but it spat out a lot of code for colours and things I couldn't fix :frown:

)

post a photo of your workings so we can tell you if we can see where you have gone wrong

Reply 2

davros

16

Original post by Azurefeline

Hi, I'm doing a 3 part question, and I've done the first two parts fine. This had led me to a (confirmed correct) question:

Show that between a and 0 the integral of (2 -e^(x) -x)dx =1 +a -0.5a^2.

I did:

integrate the equation: [2x + e^-x -0.5x^2](a_0)

Sub in values of x: [2a + e^-a -0.5a^2]-[0+e^0 -0]

Which gave me: 2a + e^-a -0.5a^2 -1.

Clearly, this must have gone wrong at some point, since it barely even has any resemblance to 1 +a -0.5a^2. Could I possibly have some help?

(Apologies, I tried to use LaTeX, but it spat out a lot of code for colours and things I couldn't fix :frown:

)

CAn you post a picture of the original question?

You're not going to get the answer shown by integrating that function because as you've spotted you need an e^a or e^-a somewhere (not sure if you are integrating e^x or e^-x!)

Reply 3

Azurefeline

OP

8

Original post by TeeEm

post a photo of your workings so we can tell you if we can see where you have gone wrong

Original post by davros

CAn you post a picture of the original question?

You're not going to get the answer shown by integrating that function because as you've spotted you need an e^a or e^-a somewhere (not sure if you are integrating e^x or e^-x!)

(Sorry, I can't type! I've edited my question.

Reply 4

davros

16

Original post by Azurefeline

(Sorry, I can't type! I've edited my question.

I can't see how that is true in general - unless there is an earlier part to the question where you showed that a satisfies some other equation which you can use to get rid of the exponential term you get when integrating!

Reply 5

Azurefeline

OP

8

Original post by davros

I can't see how that is true in general - unless there is an earlier part to the question where you showed that a satisfies some other equation which you can use to get rid of the exponential term you get when integrating!