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1OCR C2 June 2013 Q1
Use the trapezium rule, with 3 strips each of width 2, to estimate the value of the integral from 5 to 11 of (8/x) dx. [4]
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Part (a):
2EDEXCEL C2 January 2013 Q9
The finite region R, as shown in Figure 2, is bounded by the x-axis and the curve with equation y = 27 - 2x - 9 sqrt(x) - 16/x^2, x > 0. The curve crosses the x-axis at the points (1, 0) and (4, 0). (a) Complete the table below, by giving your values of y to 3 decimal places. [table: x = 1, 1.5, 2, 2.5, 3, 3.5, 4; y = 0, 5.866, blank, 5.210, blank, 1.856, 0] (2) (b) Use the trapezium rule with all the values in the completed table to find an approximate value for the area of R, giving your answer to 2 decimal places. (4) (c) Use integration to find the exact value for the area of R. (6)
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Part (b):
3EDEXCEL C2 June 2012 Q7
y = sqrt(3^x + x). (a) Complete the table below, giving the values of y to 3 decimal places. [table: x = 0, 0.25, 0.5, 0.75, 1; y = 1, 1.251, blank, blank, 2] (2) (b) Use the trapezium rule with all the values of y from your table to find an approximation for the value of the integral from 0 to 1 of sqrt(3^x + x) dx. You must show clearly how you obtained your answer. (4)
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4OCR C2 June 2012 Q6
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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5EDEXCEL C2 January 2012 Q6
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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Part (b):
6EDEXCEL C2 January 2011 Q6
y = 5/(3x^2 - 2). (a) Complete the table below, giving the values of y to 2 decimal places. [table: x = 2, 2.25, 2.5, 2.75, 3; y = 0.5, 0.38, blank, blank, 0.2] (2) (b) Use the trapezium rule, with all the values of y from your table, to find an approximate value for the integral from 2 to 3 of 5/(3x^2 - 2) dx. (4) Figure 2 shows a sketch of part of the curve with equation y = 5/(3x^2 - 2), x > 1. At the points A and B on the curve, x = 2 and x = 3 respectively. The region S is bounded by the curve, the straight line through B and (2, 0), and the line through A parallel to the y-axis. The region S is shown shaded in Figure 2. (c) Use your answer to part (b) to find an approximate value for the area of S. (3)
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7EDEXCEL C2 June 2009 Q4
(a) Complete the table below, giving values of sqrt(2^x + 1) to 3 decimal places. [table: x = 0, 0.5, 1, 1.5, 2, 2.5, 3; sqrt(2^x + 1) = 1.414, 1.554, 1.732, 1.957, blank, blank, 3] (2) Figure 1 shows the region R which is bounded by the curve with equation y = sqrt(2^x + 1), the x-axis and the lines x = 0 and x = 3. (b) Use the trapezium rule, with all the values from your table, to find an approximation for the area of R. (4) (c) By reference to the curve in Figure 1 state, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of R. (2)
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8EDEXCEL C2 January 2009 Q3
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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9EDEXCEL C2 June 2008 Q2
y = sqrt(5^x + 2). (a) Complete the table below, giving the values of y to 3 decimal places. [table: x = 0, 0.5, 1, 1.5, 2; y = blank, blank, 2.646, 3.630, blank] (2) (b) Use the trapezium rule, with all the values of y from your table, to find an approximation for the value of the integral from 0 to 2 of sqrt(5^x + 2) dx. (4)
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Part (b):
10EDEXCEL C2 June 2007 Q5
The curve C has equation y = x sqrt(x^3 + 1), 0 <= x <= 2. (a) Complete the table below, giving the values of y to 3 decimal places at x = 1 and x = 1.5. [table: x = 0, 0.5, 1, 1.5, 2; y = 0, 0.530, blank, blank, 6] (2) (b) Use the trapezium rule, with all the y values from your table, to find an approximation for the value of the integral from 0 to 2 of x sqrt(x^3 + 1) dx, giving your answer to 3 significant figures. (4) Figure 2 shows the curve C with equation y = x sqrt(x^3 + 1), 0 <= x <= 2, and the straight line segment l, which joins the origin and the point (2, 6). The finite region R is bounded by C and l. (c) Use your answer to part (b) to find an approximation for the area of R, giving your answer to 3 significant figures. (3)
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11EDEXCEL C2 June 2006 Q5
Question image is broken on examsolutions.net (dead upload, reported). The video solution below walks through the question.
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12Edexcel A Level June 2019 Paper 2 Q5
Figure 3 shows a sketch of the curve with equation y = sqrt(x). The point P(x, y) lies on the curve. The rectangle, shown shaded on Figure 3, has height y and width delta-x. Calculate the limit, as delta-x tends to 0, of the sum from x = 4 to x = 9 of sqrt(x) delta-x. (3)
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13Edexcel A Level June 2023 Paper 1 Q5
A continuous curve has equation y = f(x). The table shows corresponding values of x and y for this curve, where a and b are constants. [table: x = 3, 3.2, 3.4, 3.6, 3.8, 4; y = a, 16.8, b, 20.2, 18.7, 13.5] The trapezium rule is used, with all the y values in the table, to find an approximate area under the curve between x = 3 and x = 4. Given that this area is 17.59, (a) show that a + 2b = 51. (3) Given also that the sum of all the y values in the table is 97.2, (b) find the value of a and the value of b. (3)
