Area between 2 curves (1 Viewer)

[Zak Ambrose]

this was in my trial.

a] find the area enclosed by the y-axis, the lines y= 1, y=2 and the curve y=e^x

b] find the area enclosed by the curves y=e^x and y= ln x, and the lines y=1, y= 2.


i didn't know how to do this without using integration by parts which is definately not a 2u method. i tried to rearrange the equations etc but just ended up making a mess.

 

[blaze.bluetane]

A.

Area=2ln2-S^ln2₀e^x .dx
Area of rectangle - area under exponential

B

Similarly,
Area = S²₁e^y .dy - answer from A

Area under log w.r.t y axis(exponential when integrating) - Area already found

 

[Zak Ambrose]

thank you but i dont understand your working at all.

 

[dog on heat]

clevage

 

[blaze.bluetane]

thank you but i dont understand your working at all.

Sorry...

If you consider areas on the graph I attached above.

a] find the area enclosed by the y-axis, the lines y= 1, y=2 and the curve y=e^x
Consider the area under the curve y=e^x from 0 to ln(2). Now consider a rectangle formed by the x and y axes and the line y=2 and x=ln(2).

If we subtract the area under the curve from the area of the rectangle, we get our answer.


b] find the area enclosed by the curves y=e^x and y= ln x, and the lines y=1, y= 2.
For our first area A, we can find the area between the curve y=ln(x) and the y axis and the lines y=1 and y=2. When we integrate with respect to the y axis, the integrand becomes an exponential, which we can integrate using normal integration.

The area we are looking for is the result when our first answer from a] is subtracted from this area A

hope this helps!

 

[Zak Ambrose]

ah! thank you!. well it looks like i lost a few marks in my trial!

 

[blaze.bluetane]

ah! thank you!. well it looks like i lost a few marks in my trial!

If you did it correctly by parts it should be the same answer. Hence you should get the marks. I used MX2 polynomial stuff on a MX1 test and they gave me full marks. But I dunno... did they specify anything? If not then I don't see why parts won't get you the marks.

 

[dog on heat]

ah! thank you!. well it looks like i lost a few marks in my trial!

no wrries mate

 

[Zak Ambrose]

If you did it correctly by parts it should be the same answer. Hence you should get the marks. I used MX2 polynomial stuff on a MX1 test and they gave me full marks. But I dunno... did they specify anything? If not then I don't see why parts won't get you the marks.

well i only did a very very very very minimal amount of ext 1 maths before dropping it to get every wednesday off. so my ext 1 skills are basically shit.

 

[throwaway]

no wrries mate

how the hell areu banned and why wtf is this bullshit fucking moderators of this shithouse forum

 

[blaze.bluetane]

how the hell areu banned and why wtf is this bullshit fucking moderators of this shithouse forum

There has got to be some comedic value somewhere within all of this intense studying and schoolwork. I think it is a 'special gift' to be able to see cleavage in a log and a exponential graph, albeit completely irrelevant! I don't think I ever would have picked that up. Haha.

well i only did a very very very very minimal amount of ext 1 maths before dropping it to get every wednesday off. so my ext 1 skills are basically shit.

I think parts is MX2 but yer. Anyways I wouldn't worry about it. I'm fairly sure I wouldn't have been able to pick that answer out quickly in an exam unless I had some extra time. If thats the only one you're worried about well done.

 

[Zak Ambrose]

There has got to be some comedic value somewhere within all of this intense studying and schoolwork. I think it is a 'special gift' to be able to see cleavage in a log and a exponential graph, albeit completely irrelevant! I don't think I ever would have picked that up. Haha.



I think parts is MX2 but yer. Anyways I wouldn't worry about it. I'm fairly sure I wouldn't have been able to pick that answer out quickly in an exam unless I had some extra time. If thats the only one you're worried about well done.

well im also worried about 8 9 and 10. it was such a hard test! so much harder than the practise tests ive done!

 

[kaz1]

clevage

hahaha. Shame I can't rep you.