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1.11.2 Integrating standard functions

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Question 76

Given that $\tan x$ , use the quotient rule to show that

\frac{dy}{dx} = \sec^2 x

[3]

The cross-section of a high-precision optical lens is modeled by the region bounded by the curve $y = 3\tan^2 x + 2$ , the $x$ -axis, and the vertical boundaries $\frac{\pi}{6}$ and $\frac{\pi}{3}$ .

Show that the area of this cross-section is

3\sqrt{3} - \sqrt{3} - \frac{\pi}{6}

which simplifies to

2\sqrt{3} - \frac{\pi}{6}

Fully justify your answer.

[5]

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

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Question 76

Given that $\tan x$ , use the quotient rule to show that

\frac{dy}{dx} = \sec^2 x

[3]

The cross-section of a high-precision optical lens is modeled by the region bounded by the curve $y = 3\tan^2 x + 2$ , the $x$ -axis, and the vertical boundaries $\frac{\pi}{6}$ and $\frac{\pi}{3}$ .

Show that the area of this cross-section is

3\sqrt{3} - \sqrt{3} - \frac{\pi}{6}

which simplifies to

2\sqrt{3} - \frac{\pi}{6}

Fully justify your answer.

[5]

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.