Applications of integration

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Applications of integration

  1. 1. Group 4<br />(Alex Gagliardi) <br />Applications of Integration <br />
  2. 2. Area Under a Curve: Rectangular Approximation <br />
  3. 3. Left Rectangular Approx. Method (LRAM)<br />Right Rectangular Approx. Method (RRAM) <br />Midpoint Rectangular Approx. Method (MRAM <br />n= number of rectangles <br />Delta x= width of rectangle <br />in the interval [a,b]<br />MRAM is the most accurate because the area that you are finding is more accurate compared to RRAM and LRAM. <br />
  4. 4. Area Methods <br />
  5. 5. X-axis<br />Original equations: y= <br />Left Right <br />In terms of … <br />Two curves: top bottom <br />One curve below X-axis: -<br />
  6. 6. Y-axis<br />Original Equations <br />Y- axis<br />Bottom Top<br />In terms of y: …<br />Outer – inner /or right – left <br />One curve on left y-axis: <br />
  7. 7. Inverse<br />Different graph<br />y=x; x y; solve for y <br />X-axis: left right <br /> … terms of x<br />Top – bottom <br />*HINT* x=!!!!<br />
  8. 8. Volume Methods <br />
  9. 9. Disk Method <br />Revolved around the x-axis <br />Disk- “cylinders” <br />r= the function value <br />*always square the radius a.k.a the function value <br />
  10. 10. Washer Method <br />Y-axis<br /> in terms of y: <br />Outer curve – inner curve<br />dy or dx<br />
  11. 11. Shell Method <br />Rotate about the y-axis <br />top curve -bottom curve <br />In terms of x<br />dy or/ dx<br />
  12. 12. Area is connected to Rectangular approximation method because both involve finding the area under a curve or within a curve. <br />How is Area linked to Rectangular Approximation Method? <br />