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(a) Using the trapezium rule with seven ordinates, estimate the area of the region bounded by the curve #y=-x^2 + 6x + 1#, the lines x=0, y=0 and x=6. (b) Calculate :
(i) The area of the region in (a) above by integration.
(ii) The percentage error of the estimated area to the actual area of the region, correct to two decimal places.