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5.6.3-eg-1

# 5.6.3-eg-1 - y-values equal to each other and solve for x x...

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Example Find the area of the region bounded by the lines y = x , x = 2 and the curve y = 1 /x 2 . Solution: The graph of the region is given below: To determine the area we note the following The “upper curve” for the region is: y = x . The “lower curve” for the region is: y = 1 /x 2 . The upper range of integration is x = 2. The lower range of integration is the x -value where the line y = x intersects the curve y = 1 /x 2 . That is, we set the expressions for the
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Unformatted text preview: y-values equal to each other and solve for x : x = 1 x 2 = ⇒ x 3 = 1 = ⇒ x = 1 . The lower range of integration is x = 1. Thus the area bounded by the lines y = x , x = 2 and the curve y = 1 /x 2 , is given by Z 2 1 (upper curve-lower curve) dx = Z 2 1 ± x-1 x 2 ² dx = x 2 2-x-1-1 !³ ³ ³ ³ ³ 2 1 = x 2 2 + 1 x !³ ³ ³ ³ ³ 2 1 = 2 2 2 + 1 2 !-1 2 2 + 1 1 ! = 2 + 1 2-1 2-1 = 1 ....
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