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1.11.2 Integrating standard functions

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Question 96

Prove the identity

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

[3]

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]

Markscheme

1.11.2 Integrating standard functions Questions

A Level
Maths
1.11.2 Integrating standard functions

139 exam-style questions on AQA A Level Maths 1.11.2 Integrating standard functions. Each one has a worked solution and a mark scheme showing where the marks go.

1.11.2 Integrating standard functions

Question bank

1.11.2 Integrating standard functions

Easy Medium

Question 96

Prove the identity

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

[3]

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]

Markscheme

1.11.2 Integrating standard functions Questions

A Level
Maths
1.11.2 Integrating standard functions

139 exam-style questions on AQA A Level Maths 1.11.2 Integrating standard functions. Each one has a worked solution and a mark scheme showing where the marks go.