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Page 253 Example 1 Red line = ”over function ” = 4 – 3x.

Page 253 Example 1 Red line = ”over function ” = 4 – 3x. Blue line = ”under function ” = 3x 2 – 3x + 1. Work out 1 – 2 = 4 – 3x – (3x 2 – 3x + 1) = 3 – 3x 2 Work out primitive function for 3 – 3x 2 . This is F(x) = 3x – x 3

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Page 253 Example 1 Red line = ”over function ” = 4 – 3x.

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  1. Page 253 Example 1 Red line = ”over function” = 4 – 3x. Blue line = ”under function” = 3x2 – 3x + 1. Work out 1 – 2 = 4 – 3x – (3x2 – 3x + 1) = 3 – 3x2 Work out primitive function for 3 – 3x2. This is F(x) = 3x – x3 Work outF(x) for x=1. This is 3.1 – 13 = 2. Call this value1. Work outF(x) for X=-1. This is 3.-1 – (-1)3. = -2 Call this value2. Value1 – value2 = 2 – (-2) = 4. Answer = 4. Area

  2. Area Beräkna arean av det område som begränsas av kurvorna Y=X2-4 och Y=2X-X2. Page 254. ”Over function” is Y=2X – X2. ”Under function” is Y=X2 – 4. Work out Y=2X – X2 – (X2 – 4). This gives Y=2X-2X2+4. Primitive function F(X) = x2 – 2x3/3 + 4X This time wehave to work out the upper and lower limits as we are not given them IN THE EXAMPLE. Thereforesolve X2-4=2X-X2. 2X2-2x-4 = 0  X2-x-2 = 0  (x-2)(x+1)=0 X1 = 2 and x2 = -1

  3. Area Primitive function F(X) = x2 – 2x3/3 + 4X X1 = 2 and x2 = -1 Work out F(X) for X=2. This gives 4 – 2.8/3 + 8 = 20/3. Work out F(X) for X=-1. This gives 1 – (2.-13)/3 + 4.-1 = 1+(2/3)-4. This gives 2/3 – 3 = -7/3. Answer= F(2) – F(-1) = 9 Note: Ifthere is no ”over function” and ”under function” pleasesee page 258

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