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Please help me with this problem.

# A wire of cross sectional area a, length L and young’s modulus Y is extended by an external force F. What is the total energy stored in the wire?

I solved it in the following way:

Energy stored = ½ x stress x strain

= (½) x (F/a) x (dL/L)

= (½) x (F/a) x (F/aY)

= (1/2) x (F^2/a^2Y)

Is it right? But the answer given in my book is ½(YF^2L/a).

Here the symbol ^ represents power and x represents multiplication.

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