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1.8 Integration

1.8 Integration

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Question 218
i.

Determine ∫sin⁡2θ1+sin⁡θ dθ\int \frac{\sin 2\theta}{1 + \sin \theta} \, d\theta∫1+sinθsin2θ​dθ

[4]
ii.

A research team monitors the rate of energy consumption, EEE (in gigajoules per hour), of a large-scale data center. The rate is modeled by the function f(t)=18t2t+3f(t) = \frac{18t}{\sqrt{2t + 3}}f(t)=2t+3​18t​, where ttt is the time in hours since midnight.

Use the substitution u=2t+3u = \sqrt{2t + 3}u=2t+3​ to show that

∫18t2t+3 dt=2(2t+3)12(At+B)+k \int \frac{18t}{\sqrt{2t + 3}} \, dt = 2(2t + 3)^{\frac{1}{2}}(At + B) + k ∫2t+3​18t​dt=2(2t+3)21​(At+B)+k

where AAA and BBB are integers to be found and kkk is an arbitrary constant.

[6]
Markscheme

1.8 Integration Questions

  1. A Level
  2. /Maths
  3. /1.8 Integration

438 exam-style questions on OCR A Level Maths 1.8 Integration, covering 1.8.1 Fundamental theorem of calculus (A-level only), 1.8.2 Integrating x^n, 1.8.3 Integrating standard functions (A-level only), 1.8.4 Evaluating definite integrals, 1.8.5 Area between a curve and the x-axis, 1.8.6 Area between two curves, 1.8.7 Integration as the limit of a sum (A-level only), 1.8.8 Integration by substitution (A-level only), 1.8.9 Integration by parts (A-level only), 1.8.10 Use of partial fractions in integration (A-level only), 1.8.11 Differential equations with separable variables (A-level only), 1.8.12 Interpreting the solution of a differential equation (A-level only), and 1.8 Integration. Each one has a worked solution and a mark scheme showing where the marks go.

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