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The diagram shows a sketch of parts of the curves \(y = \frac { 16 } { x ^ { 2 } }\) and \(y = 17 - x ^ { 2 }\).
- Verify that these curves intersect at the points \(( 1,16 )\) and \(( 4,1 )\).
- Calculate the exact area of the shaded region between the curves.