Question

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

Answer 1

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	y2	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))
      −¹⁶/₃+ ⁷/₃ 
      = 7¹/₃ sq. units
   2. Percentage error
      0.0208 × 100
         ²²/₃
      =0.2836%