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The diagram shows part of the curve \(y = \sin \sqrt { x }\). This part of the curve intersects the \(x\)-axis at the point where \(x = a\).
- State the exact value of \(a\).
- Using the substitution \(u = \sqrt { x }\), find the exact area of the shaded region in the first quadrant bounded by this part of the curve and the \(x\)-axis.