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# Fp2 integration question watch

1. .

The square root in the denominator is over everything. So In the previous part of the question I worked out that the derivative of is .

so I called the f(x), so then what I want to integrate is essentially f(2x), so then I just replaced all the x values in y=... by 2x, but then when I substitute in the limits I get the wrong answer. Any hints?

2. (Original post by Music99)
Any hints?
Do you get twice what the answer should be by any chance?
3. (Original post by Music99)
.

The square root in the denominator is over everything. So In the previous part of the question I worked out that the derivative of is .

so I called the f(x), so then what I want to integrate is essentially f(2x), so then I just replaced all the x values in y=... by 2x, but then when I substitute in the limits I get the wrong answer. Any hints?

Try a substitution that gets your integral in the form of the derivative you found.
4. (Original post by ghostwalker)
Do you get twice what the answer should be by any chance?
I end up with . the root 10 bit seems really out of place, but I double checked it and it gives the correct value for what I have as the integral.
5. (Original post by Music99)
I end up with . the root 10 bit seems really out of place, but I double checked it and it gives the correct value for what I have as the integral.
I got

6. (Original post by ghostwalker)
I got

That is.
7. (Original post by ghostwalker)
I got

That is. Maybe I just subbed it in wrong or something, I'm confused now :P.
8. (Original post by BabyMaths)
That is.
Thanks.

(Original post by Music99)
That is. Maybe I just subbed it in wrong or something, I'm confused now :P.
Post working?
9. (Original post by ghostwalker)
Thanks.

Post working?
im on my phone so can't latex, but what I did was in the equation with y=... Everywhere there is an x I replaced it with a 2x then subbed in the limits.
10. (Original post by Music99)
im on my phone so can't latex, but what I did was in the equation with y=... Everywhere there is an x I replaced it with a 2x then subbed in the limits.
Safest way would be to use a subsitution, u=2x, so du/dx =2, and convert the limits. Then you'll have the exact form for the integral.
11. (Original post by ghostwalker)
Safest way would be to use a subsitution, u=2x, so du/dx =2, and convert the limits. Then you'll have the exact form for the integral.
Ah okay, also on questions like this one how do you know what substitution to use? I mean I know it comes from experience but is there a general rule of thumb.
12. (Original post by Music99)
Ah okay, also on questions like this one how do you know what substitution to use? I mean I know it comes from experience but is there a general rule of thumb.
Just compare corresponding parts of the formulae, and it should be obvious. You were aware of it when you initially thought of replacing x with 2x.

It may be an interesting exercise to see how your original methodology didn't give the correct answer,
13. (Original post by Music99)
I end up with . the root 10 bit seems really out of place, but I double checked it and it gives the correct value for what I have as the integral.
I'm struggling to see how you can get a factor in there!

If you follow the advice given and set u = 2x then your upper integration limit becomes so when you work out this just gives you a factor 1/2. If you'd accidentally left in , you'd be taking the square root of 13/16, so I'm struggling to manufacture a 10 from somewhere
14. (Original post by davros)
I'm struggling to see how you can get a factor in there!

If you follow the advice given and set u = 2x then your upper integration limit becomes so when you work out this just gives you a factor 1/2. If you'd accidentally left in , you'd be taking the square root of 13/16, so I'm struggling to manufacture a 10 from somewhere
I think I must have typed it in wrong on the calculator or something.
15. (Original post by Music99)
I think I must have typed it in wrong on the calculator or something.
OK, are you happy about following the suggestion made by Ghostwalker and how to get the correct answer now?
16. (Original post by davros)
OK, are you happy about following the suggestion made by Ghostwalker and how to get the correct answer now?
Yes .

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