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Math Help - Really need help with these questions

  1. #1
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    Really need help with these questions

    1.I need to evaluate (x+x^3)dx with limits 2 and 1

    ii. estimate the above integral using the trapezium rule using 5 strips

    2.i need to use the trapezium rule with 4 strips to estimate root(1+x^2) with limits of 4 and 0

    3.the gradient function is dy/dx= 1/x^2 - xrootx

    4.I need to find the stationary point of the graph y= (1/x) + (1/x^2) - (1/x^3) and need to determine their natures of each

    I need help with these 4 please. Dont think you have to answer them all, but i do need all the answers and working out Thanks

    Need replies ASAP
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  2. #2
    MHF Contributor
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    Well, do it, Good Fellow.

    Given f(x) = x + x^3 and 5 strips, you will need:

    f(1)
    f(1.2)
    f(1.4)
    f(1.6)
    f(1.8)
    f(2)

    Let's see what you get.
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  3. #3
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    thats the thing i dont have a clue and need to know if i want to keep my head
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  4. #4
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    ive done the bit in the table but now need to apply the rule. help?
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  5. #5
    MHF Contributor
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    You'll never get it with a screen name like that.

    1.2 - 1.0 = 0.2
    1.4 - 1.2 = 0.2
    1.6 - 1.4 = 0.2
    1.8 - 1.6 = 0.2
    2.0 - 1.8 = 0.2

    This makes it appears as though the interval width is 0.2.

    Now build the little trapezoids.

    Here's the first one.
    0.2*(f(1.0)+f(1.2))/2

    Let's see what you get for the rest.
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