4.08h Integration: inverse trig/hyperbolic substitutions

79 questions

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WJEC Further Unit 4 2022 June Q7
8 marks Challenging +1.2
  1. Express \(4x^2 + 10x - 24\) in the form \(a(x + b)^2 + c\), where \(a\), \(b\), \(c\) are constants whose values are to be found. [3]
  2. Hence evaluate the integral $$\int_3^5 \frac{6}{\sqrt{4x^2 + 10x - 24}} dx.$$ Give your answer correct to 3 decimal places. [5]
SPS SPS FM 2021 November Q5
4 marks Standard +0.8
Use a trigonometrical substitution to show that $$\int_0^2 \frac{1}{(16 - x^2)^{\frac{3}{2}}} dx = \frac{1}{16\sqrt{3}}$$ [4 marks]
SPS SPS FM Pure 2026 November Q7
4 marks Standard +0.8
In this question you must show detailed reasoning. Evaluate \(\int_0^{\frac{1}{2}} \frac{2}{x^2 - x + 1} dx\). Give your answer in exact form. [4]
OCR Further Pure Core 1 2021 June Q5
7 marks Challenging +1.2
In this question you must show detailed reasoning. Find \(\int_{-1}^{11} \frac{1}{\sqrt{x^2 + 6x + 13}} dx\) giving your answer in the form \(\ln(p + q\sqrt{2})\) where \(p\) and \(q\) are integers to be determined. [7]