Download MEI C2 Study Resources Core2 Integration 1-2 by Bob Sheehan PDF

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Extra resources for MEI C2 Study Resources Core2 Integration 1-2

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Y x P (i) Find the coordinates of the point P. (ii) Find the gradient of the curve at P. (iii) Find the shaded area. [2] [2] [5] 5. (i) Sketch the curve y = 2 − x − x2. (ii) Find the area enclosed by the curve and the x-axis between x = 0 and x = 2. 6. The diagram shows a cross-section of a tunnel. 5 metres along the cross section. Use the trapezium rule to estimate the area of the cross-section. 35 Is it an under-estimate or over-estimate? 5 [5] © MEI, 07/04/09 1/2 MEI C2 Integration Assessment 7.

Y  x( x  1) The graph cuts the x-axis at the origin and the point (1, 0). y This area is negative as it is below the x-axis. x 1 2 © MEI, 29/06/10 The areas above and below the x-axis must be calculated separately. 2/5 MEI C2 Integration Section 2 Exercise solutions 1 Area below x-axis   x( x  1)dx 0 1   ( x 2  x )dx 0 1   31 x 3  21 x 2  0  31  21   61 2 Area above x-axis   31 x 3  21 x 2  1   83  2    31  21   56 Total area  61  56  1 square unit. 5. y  x 2  2 x  3  ( x  3)( x  1) y x -3 -1 3 1 Area above x-axis   ( x 2  2 x  3) dx 3 1   31 x 3  x 2  3 x  3    31  1  3    9  9  9  32 3 3 Area below x-axis   31 x 3  x 2  3 x  1   9  9  9    31  1  3   9  53   323 Total area  323  323  64 3 square units 6.

To build up the puzzle, place together the edges on which an integral and its solution are written, so that the triangles are joined along this edge. Begin by just finding pairs of integrals and solutions and placing them edge-to-edge. As you progress you will find that all of the pieces will eventually link up to form a large hexagon. By all means try this by yourself, but it is really designed to be a group activity. Working with other students will help to highlight any misconceptions you may have, as well as making the task more enjoyable.

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