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    There's a trapezium rule question on one of the Solomon papers that I just cannot get right. Could someone else have a go at it, because I seriously cannot see where I am going wrong...

    Use the trapezium rule with four intervals of equal width to estimate the area of the shaded region (its bound by the origin and x = 2) on the curve y=4x^{\frac{1}{2}}e^{-x}.
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    (Original post by ljfrugn)
    There's a trapezium rule question on one of the Solomon papers that I just cannot get right. Could someone else have a go at it, because I seriously cannot see where I am going wrong...

    Use the trapezium rule with four intervals of equal width to estimate the area of the shaded region (its bound by the origin and x = 2) on the curve y=4x^{\frac{1}{2}}e^{-x}.
    Well I get 2.33... but I'm just guessing. :p:
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    (Original post by Vijay1)
    Well I get 2.33... but I'm just guessing. :p:
    I get that answer too:

    (f(0) + 2f(0.5) + 2f(1) + 2f(1.5) + f(2))/4

    where f(x) = 4x^(1/2)e^(-x).
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    (Original post by Jonny W)
    I get that answer too:

    (f(0) + 2f(0.5) + 2f(1) + 2f(1.5) + f(2))/4

    where f(x) = 4x^(1/2)e^(-x).

    Yes.

    0
    1.716*2
    1.4715*2
    1.093*2
    0.766

    Total 9.327*0.25 = 2.33

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    Yep, same as what I get, the mark scheme gets it as 2.41. Their values in the table are the same as mine, except for the '2' value, which for me is 0.76557, but they get 1.083. I take it that their answer is wrong then?
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    wot IS the trapezium rule?
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    (Original post by ljfrugn)
    Yep, same as what I get, the mark scheme gets it as 2.41. Their values in the table are the same as mine, except for the '2' value, which for me is 0.76557, but they get 1.083. I take it that their answer is wrong then?
    I would say so.

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    (Original post by lesser weevil)
    wot IS the trapezium rule?
    A method of approximating an integral by dividing the area up into trapezia and considering the curve between each of these strips to be a straight line, so you can find the area by adding the areas of the trapezia.
    http://en.wikipedia.org/wiki/Trapezium_rule
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    (Original post by lesser weevil)
    wot IS the trapezium rule?
    It's a way to estimate the area under a curve (between specified limits) when direct integration is not a realistic route.

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    mark scheme is probably wrong. It happens.
 
 
 
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