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anonymous

  • one year ago

Write the summation to estimate the area under the curve y = 1 + x^2 from x = –1 to x = 2 using 3 rectangles and right endpoints.

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  1. anonymous
    • one year ago
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    https://gyazo.com/d4d434542599aa197b53e5f947deb365

  2. anonymous
    • one year ago
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    @zzr0ck3r

  3. zzr0ck3r
    • one year ago
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    so where will out summation start?

  4. zzr0ck3r
    • one year ago
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    remember we go to the right of the first interval

  5. zzr0ck3r
    • one year ago
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    the intervals here are -1,0 0,1 1,2

  6. anonymous
    • one year ago
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    Would we not need to divide into four intervals? That's what I got from you from the other posts.

  7. anonymous
    • one year ago
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    Three rectangles = three intervals

  8. anonymous
    • one year ago
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    I feel stupid....thanks @SithsAndGiggles

  9. anonymous
    • one year ago
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    So can you also explain the right or left endpoints? My AP Calc teacher last year never taught us anything like this.

  10. anonymous
    • one year ago
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    Sure. I found I learned it best with a visual representation (which I'll be doing in parts for color-coding purposes) |dw:1441158115140:dw|

  11. anonymous
    • one year ago
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    So the point here is to find the area under the curve, but suppose we don't know the various rules for antiderivatives. Instead, we can approximate the area using rectangles (among other shapes), like so: |dw:1441158222375:dw|

  12. anonymous
    • one year ago
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    The area under the curve is then *approximately* equal to the total area under the curve. The "left/right endpoint" approximations refer to those that use rectangles that are determined by their left/right endpoints. For your question, you're looking at the right endpoints: |dw:1441158349598:dw|