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CIE 9709 2024 June Paper 33 Q11

A Level / CIE / P3

CIE 9709 2024 June Paper 33 Paper · Question 11

题目

Problem

Use the substitution 2x=tan⁡θ2x=\tan\theta to find the exact value of

∫01212(1+4x2)2 dx.\int_0^{\frac12}\frac{12}{(1+4x^2)^2}\,\mathrm{d}x.

Give your answer in the form a+bπa+b\pi, where aa and bb are rational numbers.

(9)
题目中文翻译

使用代换 2x=tan⁡θ2x=\tan\theta,求

∫01212(1+4x2)2 dx\int_0^{\frac12}\frac{12}{(1+4x^2)^2}\,\mathrm{d}x

的精确值。

将答案表示为 a+bπa+b\pi 的形式,其中 aa 和 bb 为有理数。

(9)
原卷通用作答要求

Answer all questions. You should use a calculator where appropriate.

You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator.

Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.

请回答所有题目。适当时应使用计算器。必须清楚展示所有必要的计算过程;仅给出计算器答案而没有过程,不予评分。除非题目另有精度要求,非精确数值答案保留 3 位有效数字,以度为单位的角度保留 1 位小数。

解答