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5 marksIntegration I

CAPE Pure Mathematics Unit 1 · May/June 2001 · Paper 2 · Question 6(b)(ii)

The region, R, is bounded by the curve y = x² + 1, the x-axis, and the lines x = 0 and x = 2.

The area of R is estimated using the trapezium rule with 2 intervals of equal width. Show that this trapezium rule estimate differs by 1/3 from the exact value for the area of R found in (b)(i).

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Other parts of this question

  1. 6(a)Calculate the volume generated when the finite region in the first quadrant bounded by the curve, y = 2x², the y-axis and the line y = 2 is rotated completely…[6 marks]
  2. 6(b)(i)Calculate the area of R.[5 marks]
  3. 6(b)(iii)On a carefully labelled sketch of y = x² + 1, shade in the 2 trapezia which are used to estimate the area of R.[4 marks]
  4. 6(b)(iv)Another approximation for the area of R is obtained using 2 trapezia of unequal width. The first trapezium has width, h, and the second trapezium width, (2 -…[5 marks]

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