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1.8.2 Integration

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Question 7
a.

Find ∫(12x2−5xx) dx\int \left( 12x^2 - \dfrac{5}{x\sqrt{x}} \right) \, dx ∫(12x2−xx​5​)dx

[3]
b.

The rate of change of the mass, MMM grams, of a chemical precipitate over time ttt minutes is modelled by the differential equation

dMdt=12t2−5tt,t>0 \dfrac{dM}{dt} = 12t^2 - \dfrac{5}{t\sqrt{t}}, \quad t > 0 dtdM​=12t2−tt​5​,t>0

Given that at t=4t = 4t=4, the mass of the precipitate is 265 grams, determine an expression for MMM in terms of ttt.

[3]

1.8.2 Integration Questions

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