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Q8. (a) A gas expands in a cylinder according to the relationship PV^1.25 = 1294.

The initial volume of the gas is 0.05m³ and the final volume of the gas is 0.105m³.

Calculate the work done by the gas during the expansion.

Note: the work done by the gas as it expands from V₁ to V₂ units of volume is

W Joules, where W = ∫_V1^V2)PdV.   (8)

(b) Given dy/dx = 3x² + 4x + 1 - 3/x² and y = 19 when x = 2,

Determine the value of y when x = - 1.     (8)