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$9 AS Mathematics Integration Section 2: Area under a curve Exercise level 2 1. Evaluate: (i) f2(x+3)(x2)dx (ii) I: x(x2 +1)dx Find the total area enclosed by y = )52 2x 3 , the x axis, x = 3 and x = 3. Find the total area enclosed by y = x(x 1) , the x axis and the line x = 2 . (i) Sketch the curve y = x3 x for values of x from 3 to +3. (ii) Find the area bounded by the curve, the x axis and the lines x =1 and x = 2. (iii) Find the area bounded by the curve and the lines x = 1 , x = 0 and the x axis. (iv) From your answers to (ii) and (iii) and your sketch deduce the total area given by the integral I: (x3 x)dx . Explain your reasoning. (i) Sketch the general shape of curve y = x(x + 2)(x 3) showing where it crosses the x-axis. (ii) Find the total area enclosed between the graph and the x-axis. Find the area enclosed by the curve y = (x 3)2 and the lines y = 0 and y = 4 . Find the total area enclosed by the curve y = x(4 x2) and the x-axis