2．（a）On the same diagram，sketch \(y = x\) and \(y = \sqrt { } x\) ，for \(x \geq 0\) ，and mark clearly the coordinates of the points of intersection of the two graphs．
（b）With reference to your sketch，explain why there exists a value \(a\) of \(x ( a > 1 )\) such that $$\int _ { 0 } ^ { a } x \mathrm {~d} x = \int _ { 0 } ^ { a } \sqrt { } x \mathrm {~d} x$$ （c）Find the exact value of \(a\) ．
（d）Hence，or otherwise，find a non－constant function \(\mathrm { f } ( x )\) and a constant \(b ( b \neq 0 )\) such that $$\int _ { - b } ^ { b } \mathrm { f } ( x ) \mathrm { d } x = \int _ { - b } ^ { b } \sqrt { } [ \mathrm { f } ( x ) ] \mathrm { d } x$$