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The definite integral

denotes the difference in value of f ( x ) between x = a and x = b . The definite integral. If . Then . In other words. Notationally we write. Example Evaluate ( i ) (ii) (iii) (iv) (v) (vi). y. Example The Line drawn below is of y = 2 x – 4

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The definite integral

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  1. denotes the difference in value of f(x) between x = a and x = b The definite integral If Then

  2. In other words Notationally we write

  3. Example Evaluate (i) (ii) (iii) (iv) (v) (vi)

  4. y Example • The Line drawn below is of y = 2x – 4 • The shaded region is bounded between the graph, the x-axis and the lines x = 2 and x = 4. • Using two methods show that the area shaded is 4 0 4 2 x

  5. y a b x Area Under a graph • The area enclosed between the graph of a function, the x-axis and the ordinates drawn at x = a and x = b is given by the formula

  6. y 0 x Example The sketch is of the graph . Shade the area enclosed between the graph, and the x-axis from x = 0 to x = 1. Calculate this area.

  7. y 0 x Example The Sketch is of the graph of Show that the curve cuts the x axis at x = –2, x = 0 and x = 1. Hence obtain the area of the finite region between the curve and the x-axis and the ordinates x = –2 and x = 0 .

  8. y 0 x 1. A level Past paper question The Curve C has equation   The diagram shows a sketch of the curve C in the first quadrant. Calculate the area of the shaded region.

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