1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only)

a.

Prove the identity

\frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x

[3]

b.

The rate of airflow $R\,$ into a mechanical respirator, in litres per second, is modeled by the function

\frac{10 \sin 6t}{1 + \tan^2 3t}

where $t\,$ is the time in seconds. Find an expression for the total volume of air $\int R(t) \, dt$ .

[4]

a.

Prove the identity

\frac{\sin 2x}{1 + \tan^2 x} \equiv 2 \sin x \cos^3 x

[3]

b.

The rate of airflow $R\,$ into a mechanical respirator, in litres per second, is modeled by the function

\frac{10 \sin 6t}{1 + \tan^2 3t}

where $t\,$ is the time in seconds. Find an expression for the total volume of air $\int R(t) \, dt$ .

[4]

1.9.24 Integrate e^kx, 1/x, sin kx, cos kx (A-level only) Questions