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Example 3 Find the area A between the parabola y = x 2 and the line y = x+6 .

Example 3 Find the area A between the parabola y = x 2 and the line y = x+6 . Solution The first step is to determine the intersection points of this line and parabola: x 2 = x+6, 0= x 2 - x- 6 = ( x-3 )( x+2 ). Hence the intersection points are x=3 and x=-2. Then

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Example 3 Find the area A between the parabola y = x 2 and the line y = x+6 .

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  1. Example 3 Find the area A between the parabola y = x2and the line y = x+6. Solution The first step is to determine the intersection points of this line and parabola: x2 = x+6, 0= x2 - x- 6 = (x-3)(x+2). Hence the intersection points are x=3 and x=-2. Then Since D(x3/3 - x2/2 – 6x) = x2 - x - 6,

  2. An alternative approach to the preceding computation begins by sketching the region between parabola y = x2and the line y=x+6. From this sketch, we see that x+6  x2for –2  x  3. Hence y = x2

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