Calculus

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Estimate the area under the curve f(x)=x^2 between x=0 and x=1 using 4 rectangles of equal width if

a) The height is taken from the right endpoint

b) The height is taken from the midpoint.

I have no idea what exactly this question is asking me to do is this suppose to be a bar graph?

  • Calculus -

    You want to find the area under the curve. The easy thing for doing area is a rectangle: width*height.

    So, divide the interval into 4 sections of equal width, and use y as the height. But which y? on the left side, right side, in the middle, or what? Doesn't matter; pick one and try it.

    If you have no idea what is wanted, you haven't listened in class, or read the material, or both. Or (gasp!) gone online to study up on the topic.


    Below are tables showing the iteration number, x,y values, and partial sum.

    RIGHT-HAND RULE:
    1: (0.2500,0.0625) 0.01562
    2: (0.5000,0.2500) 0.07812
    3: (0.7500,0.5625) 0.21875
    4: (1.0000,1.0000) 0.46875

    MIDPOINT RULE:
    1: (0.1250,0.0156) 0.00391
    2: (0.3750,0.1406) 0.03906
    3: (0.6250,0.3906) 0.13672
    4: (0.8750,0.7656) 0.32812


    Actual value: 0.33333

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