1.7 Integration

Determine $dt\int \left( 10t^4 - \frac{6}{\sqrt[3]{t}} \right) \, dt$ .

[3]

The rate of change of the mass, $M$ grams, of a synthetic crystal with respect to time, $t$ hours, is modeled by the differential equation

\frac{dM}{dt} = 10t^4 - \frac{6}{\sqrt[3]{t}}, \quad t > 0

After 8 hours of growth, the mass of the crystal is measured to be 65520 grams.

Find an expression for $M$ in terms of $t$ .

[3]

1.7 Integration Questions

Determine $dt\int \left( 10t^4 - \frac{6}{\sqrt[3]{t}} \right) \, dt$ .

[3]

The rate of change of the mass, $M$ grams, of a synthetic crystal with respect to time, $t$ hours, is modeled by the differential equation

\frac{dM}{dt} = 10t^4 - \frac{6}{\sqrt[3]{t}}, \quad t > 0

After 8 hours of growth, the mass of the crystal is measured to be 65520 grams.

Find an expression for $M$ in terms of $t$ .

[3]