1.9.28 Integration by substitution (other cases) (A-level only)

The rate of change of the mass of a substance in a chemical reaction, $M^{'} (t)$ in grams per hour, is modeled by the function:

\frac{18t}{\sqrt{3t+4}}, \quad 0 \le t \le 4

Using the substitution $\sqrt{3t+4}$ , find the exact change in mass, in grams, between $t = 0$ and $t = 4$ .

[6]

ii.

In a separate experiment, the pressure within a vessel is found to vary according to the function:

\frac{6p^2 - 11}{(p - 1)(3p + 2)}

Find $dp\int f(p) \, dp$ .

[5]

1.9.28 Integration by substitution (other cases) (A-level only) Questions

The rate of change of the mass of a substance in a chemical reaction, $M^{'} (t)$ in grams per hour, is modeled by the function:

\frac{18t}{\sqrt{3t+4}}, \quad 0 \le t \le 4

Using the substitution $\sqrt{3t+4}$ , find the exact change in mass, in grams, between $t = 0$ and $t = 4$ .

[6]

ii.

In a separate experiment, the pressure within a vessel is found to vary according to the function:

\frac{6p^2 - 11}{(p - 1)(3p + 2)}

Find $dp\int f(p) \, dp$ .

[5]