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# P2 help watch

1. Can you check if I got this right?

∫ [√(e^2x + 4)] dx, where the intergral is between 1.5 and 0.

I used the trapezium rule and used an interval of 3, got an estimate of 11.120 (3dp) I'm not sure if this is correct.
2. (Original post by 2776)
Can you check if I got this right?

∫ [√(e^2x + 4)] dx, where the intergral is between 1.5 and 0.

I used the trapezium rule and used an interval of 3, got an estimate of 11.120 (3dp) I'm not sure if this is correct.
Give me one second, is that using 2 or 4 strips?
3. (Original post by 2776)
Can you check if I got this right?

∫ [√(e^2x + 4)] dx, where the intergral is between 1.5 and 0.

I used the trapezium rule and used an interval of 3, got an estimate of 11.120 (3dp) I'm not sure if this is correct.
Also, is that e^(2x+) or (e^2x)+4?
4. (Original post by Bhaal85)
Give me one second, is that using 2 or 4 strips?
3 strips apparently
5. (Original post by 2776)
Can you check if I got this right?

∫ [√(e^2x + 4)] dx, where the intergral is between 1.5 and 0.

I used the trapezium rule and used an interval of 3, got an estimate of 11.120 (3dp) I'm not sure if this is correct.
'n' intervals = (n+1) ordinates
6. i get 4.603 (but it's been a while since i did the trapezium rule)
7. (Original post by Bhaal85)
Also, is that e^(2x+) or (e^2x)+4?
Its the second one, and also the square root.
8. I got 4.76930
9. (Original post by Bhaal85)
I got 4.76930
X 0 0.5 1 1.5
Y 5^(1/2) 2.59196 3.37477 4.90770

h=0.5

0.5/2 * (5^(1/2)+4.90770+2(2.59196+3.37477))
10. as a good estimate (with h = 0.005, ie 300 steps) i got 4.693638381
11. (Original post by elpaw)
as a good estimate (with h = 0.005, ie 300 steps) i got 4.693638381
Why not integrate the whole equation then find the exact answer? Then use only 2 strips. Then we can route out what should be right and what is wring. I think we can agree that the initial answer given by 2776 of 12........ is wrong though.
12. (Original post by Bhaal85)
X 0 0.5 1 1.5
Y 5^(1/2) 2.59196 3.37477 4.90770

h=0.5

0.5/2 * (5^(1/2)+4.90770+2(2.59196+3.37477))
13. (Original post by Bhaal85)
Why not integrate the whole equation then find the exact answer?
it is a tricky integral that would either require a laplace transform, or a series expansion, and it is beyond p6 methings
14. (Original post by 2776)
I actually used indents to space out the numbers, this Vbulletin board must have changed the format. Damn. Oh well, at least you know what I meant.
15. (Original post by elpaw)
it is a tricky integral that would either require a laplace transform, or a series expansion, and it is beyond p6 methings
I thought that it would be within your abilities. I actually got confused for one moment and began using the chain rule to differentiate, before realising that I had to integrate and had not done it before. lol. Ah, the joy of maths.
16. Integrated it on my calcuator, and it comes to exactly 4.6936. So Bhaal, you are correct.

I was wondering about this, how do you integrate this in terms of e and pi:

∫ [∏(√e^2x +4)²] between 1.5 and 0.

I got something similar to this:

∫(∏ (e^2x + 4)) but can you integrate e?
17. (Original post by 2776)
Integrated it on my calcuator, and it comes to exactly 4.6936. So Bhaal, you are correct.

I was wondering about this, how do you integrate this in terms of e and pi:

∫ [∏(√e^2x +4)²] between 1.5 and 0.

I got something similar to this:

∫(∏ (e^2x + 4)) but can you integrate e?
Yes you can integrate e^x. E.g to integrate e^mx where 'm' is a constant, its (e^mx)/m
18. (Original post by 2776)
Integrated it on my calcuator, and it comes to exactly 4.6936. So Bhaal, you are correct.

I was wondering about this, how do you integrate this in terms of e and pi:

∫ [∏(√e^2x +4)²] between 1.5 and 0.

I got something similar to this:

∫(∏ (e^2x + 4)) but can you integrate e?
You can integrate e! Integral of e^2x = (1/2)e^2x. You didn't cover that in your P2?
19. (Original post by 2776)
Integrated it on my calcuator, and it comes to exactly 4.6936. So Bhaal, you are correct.

I was wondering about this, how do you integrate this in terms of e and pi:

∫ [∏(√e^2x +4)²] between 1.5 and 0.

I got something similar to this:

∫(∏ (e^2x + 4)) but can you integrate e?
To integrate the equations I believe you can take the pi out of the integral, as it is only a constant. so you would integrate:

∏∫ [(√e^2x +4)²] dx <------------tut tut tut tut you forgot the dx.
20. Hmm, I am supposed to give the integral in terms of pi and e. However I got to this stage:

pi [ 0.5 {e^2x} + 4x] between 0 and 1.5

And I get an answer of:

(pi*0.5*e^3 +6pi) - pi*0.5

= pi*e^3 +12pi - pi

= pi (e^3 +11)

So is this the correct answer?

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