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    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.
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    (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?
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    (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?
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    (Original post by Bhaal85)
    Give me one second, is that using 2 or 4 strips?
    3 strips apparently
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    (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
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    i get 4.603 (but it's been a while since i did the trapezium rule)
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    (Original post by Bhaal85)
    Also, is that e^(2x+) or (e^2x)+4?
    Its the second one, and also the square root.
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    I got 4.76930
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    (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))
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    as a good estimate (with h = 0.005, ie 300 steps) i got 4.693638381
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    (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.
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    (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))
    Yep, your right.
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    (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
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    (Original post by 2776)
    Yep, your right.
    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.
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    (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.
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    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?
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    (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
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    (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?
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    (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.
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    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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