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

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

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 - h) with the three ordinates occurring where x = 0, x = h and x = 2. Show that the total area of these 2 trapezia of unequal widths is given by (h² - 2h + 6).

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

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]
6(b)(i)Calculate the area of R.[5 marks]
6(b)(ii)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…[5 marks]
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]

More practice: the rest of this paper · more Integration I questions · all CAPE Pure Mathematics Unit 1 past papers