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MistaGrimm

  • 3 years ago

how do i find the finite approximation to estimate the area using the lower sum of 4 rectangles for f(x)= 4-x^2 between x=-2 and x=2?

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  1. heisenberg
    • 3 years ago
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    well i see an easy way to make 4 rectangles from -2 to 2. they each have a width of 1.

  2. heisenberg
    • 3 years ago
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    and they have a height of the minimum between f(x) and f(x+1), ie the left and right sides

  3. myininaya
    • 3 years ago
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    i do not see a way to obtain a lower sum some of the rectangles end up above the curve starting from left endpoint or starting from right endpoint

  4. myininaya
    • 3 years ago
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    i guess a lower sum does not mean all the rectangles have to be under the curve

  5. heisenberg
    • 3 years ago
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    well the first rectangle would be from -2 to -1. f(-2) = 0 f(-1) = 2 this rectangle has 0 height, therefore it has no area. A = length * width = 0. second rectangle from -1 to 0 f(-1) = 2 f(0) = 4 this rectangle has height of 2 (the minimum). area = height * width = 2 * 1 = 2 third rectangle from 0 to 1 is the same A3 = 2 fourth rectangle from 1 to 2 is the same as the first: A4 = 0 * 1 = 0 Total area = A1 + A2 + A3 + A4 = 4

  6. myininaya
    • 3 years ago
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    starting from right endpoint we do Ar=1*(f(2)+f(1)+f(0)+f(-1)] starting from left end point we do Al=1*(f(-2)+f(-1)+f(0)+f(1)]

  7. myininaya
    • 3 years ago
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    but these Ar=Al since f is even function

  8. MistaGrimm
    • 3 years ago
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    sweet, thankyou both

  9. myininaya
    • 3 years ago
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    oh wait Heisenberg i see i was only thinking of left endpoint rule and right endpoint rule and i even though of the mid point rule but we we could have chosen any number to approximate the area and since we want a lower sum we look in each of the intervals (-2,-1), (-1,0), (0,1), (1,2) and pick the sample number that gives the minimum height great job Heisenberg

  10. heisenberg
    • 3 years ago
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    ah yes. i didn't even think about those. luckily for me, it worked out. ...this time :p

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