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Use the graph to answer the question below

  1. Using trapezium rule with 7 ordinates calculate the shaded area. 
  2. Using mid ordinate rule with 6 strips, estimate the area of the shaded region.   
  3.   
    1. Calculate the actual area of the shaded region    
    2. Find the percentage error in using mid ordinate rule

1 Answer

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  1.  
     y0      y1  y2     y3  y4   y5  y6
     −4 −3.75  −3  −1.75   0 2.25  5
    ½ × ½ ( 4+5) + 2(3.75 +3+1.75+0+2.25)
    ¼ × 30.5
    =7.625 units2
  2.  
        y1    y   y3    y4   y5   y6
     x   0.25  0.15  1.25  1.75  2.25  2.75
    A=½ (3.9375+3.4375+2.4375+0.9375+(0.0625+3.5625)
         ½ × 15.375 
        =7.6875 sq units
  3.  
    1. Actual area of shaded region

      (8/3−8) + ((9−12) − (8/3−8))
      16/37/3 
      = 71/3 sq. units
    2. Percentage error
      0.0208 × 100
         22/3
      =0.2836%
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