# Maths A level

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Help with this question please. There's a diagram too, any help would be appreciatedI'm really struggling.

the region enclosed between the curves y=e^x y=6-e^x/2 and the line x=0 shown shaded in the diagram below sow that the exact area of the shaded region is 6ln4-5 fully justify your answer

the region enclosed between the curves y=e^x y=6-e^x/2 and the line x=0 shown shaded in the diagram below sow that the exact area of the shaded region is 6ln4-5 fully justify your answer

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#2

(Original post by

Help with this question please. There's a diagram too, any help would be appreciatedI'm really struggling.

the region enclosed between the curves y=e^x y=6-e^x/2 and the line x=0 shown shaded in the diagram below sow that the exact area of the shaded region is 6ln4-5 fully justify your answer

**user3.14159**)Help with this question please. There's a diagram too, any help would be appreciatedI'm really struggling.

the region enclosed between the curves y=e^x y=6-e^x/2 and the line x=0 shown shaded in the diagram below sow that the exact area of the shaded region is 6ln4-5 fully justify your answer

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#3

**user3.14159**)

Help with this question please. There's a diagram too, any help would be appreciatedI'm really struggling.

the region enclosed between the curves y=e^x y=6-e^x/2 and the line x=0 shown shaded in the diagram below sow that the exact area of the shaded region is 6ln4-5 fully justify your answer

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(Original post by

What are you stuck with (and the diagram would help ...)? The integration, finding the limits, ..

**mqb2766**)What are you stuck with (and the diagram would help ...)? The integration, finding the limits, ..

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#5

(Original post by

Hi, thanks for replying. I'm having trouble with where to begin - exponentials is something I've struggled with for a while. I'll try to upload a photo (I'm like an 80 year old when it comes to technology). It's from the aqa released documents on integration.

**user3.14159**)Hi, thanks for replying. I'm having trouble with where to begin - exponentials is something I've struggled with for a while. I'll try to upload a photo (I'm like an 80 year old when it comes to technology). It's from the aqa released documents on integration.

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#6

**user3.14159**)

Hi, thanks for replying. I'm having trouble with where to begin - exponentials is something I've struggled with for a while. I'll try to upload a photo (I'm like an 80 year old when it comes to technology). It's from the aqa released documents on integration.

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(Original post by

You obviously need to know how to integrate exponentials to answer the question. Similarly, if R is defined by where they interect, you'll need to find that point. Post what youve tried.

**mqb2766**)You obviously need to know how to integrate exponentials to answer the question. Similarly, if R is defined by where they interect, you'll need to find that point. Post what youve tried.

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#10

(Original post by

Would I just integrate the values or use substitution?

**user3.14159**)Would I just integrate the values or use substitution?

As laurawatt says, if you're ok with that, you can consider R as being the difference of two areas.

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(Original post by

Can you integrate the functions individually?

As laurawatt says, if you're ok with that, you can consider R as being the difference of two areas.

**mqb2766**)Can you integrate the functions individually?

As laurawatt says, if you're ok with that, you can consider R as being the difference of two areas.

Last edited by user3.14159; 1 month ago

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#12

(Original post by

I think I may have done it wrong but is it just 6x-2e^x/2 + C

**user3.14159**)I think I may have done it wrong but is it just 6x-2e^x/2 + C

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(Original post by

You can always differentiate your answer to check, but that looks ok for the indefinite integral of the "harder" function.

**mqb2766**)You can always differentiate your answer to check, but that looks ok for the indefinite integral of the "harder" function.

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#14

(Original post by

Yeah, I'm alright with that integration but I'm not sure what the next steps are

**user3.14159**)Yeah, I'm alright with that integration but I'm not sure what the next steps are

Last edited by mqb2766; 1 month ago

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(Original post by

Tbh, finding the area of a region like this is a reasonably common question and if you're attempting exam practice questions, you should have come across similar ones before? Laurawatt's post gave the formula, so it involves integrating the difference of two functions between a and b. What does that mean for this question - what is the upper / lower function, what are the limits of the definite integral?

**mqb2766**)Tbh, finding the area of a region like this is a reasonably common question and if you're attempting exam practice questions, you should have come across similar ones before? Laurawatt's post gave the formula, so it involves integrating the difference of two functions between a and b. What does that mean for this question - what is the upper / lower function, what are the limits of the definite integral?

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#16

**user3.14159**)

Yeah, I'm alright with that integration but I'm not sure what the next steps are

The integration which you did above is correct but you also need to take into account the fact that the region is bounded by two curves not just one. So you need to do the integral of (f(x) - g(x)) dx which you can easily visualise which is f(x) and which is g(x) given the diagram and the area (region) required.

Last edited by MiladA; 1 month ago

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#17

(Original post by

I'm not sure how to determine the upper and lower, limits of the definite integral, the question is posted on this thread but I don't know how to find these out?

**user3.14159**)I'm not sure how to determine the upper and lower, limits of the definite integral, the question is posted on this thread but I don't know how to find these out?

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(Original post by

Do you understand what they represent? The x-values where the integral starts and finishes. One is "obvious" as its simple and given in the question. The other needs to be calculated using a fact.

**mqb2766**)Do you understand what they represent? The x-values where the integral starts and finishes. One is "obvious" as its simple and given in the question. The other needs to be calculated using a fact.

Last edited by user3.14159; 1 month ago

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#19

(Original post by

One of them would be x=0 I think

**user3.14159**)One of them would be x=0 I think

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(Original post by

of course. What gives the upper limit?

**mqb2766**)of course. What gives the upper limit?

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