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1.11.2 Integrating standard functions

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Question 94

Show that the trigonometric identity

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

is valid for all $x\,$ where the expression is defined.

[3]

In a wave mechanics simulation, the rate of change of energy density $E\,$ with respect to phase $ϕ\phi$ (in radians) is modeled by the equation:

\frac{dE}{d\phi} = \frac{30 \sin 6\phi}{1 + \tan^2 3\phi}

Hence, determine the general expression for $E(ϕ)E(\phi)$ .

[6]

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 94

Show that the trigonometric identity

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

is valid for all $x\,$ where the expression is defined.

[3]

In a wave mechanics simulation, the rate of change of energy density $E\,$ with respect to phase $ϕ\phi$ (in radians) is modeled by the equation:

\frac{dE}{d\phi} = \frac{30 \sin 6\phi}{1 + \tan^2 3\phi}

Hence, determine the general expression for $E(ϕ)E(\phi)$ .

[6]

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.