Integration
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Question 427
The region R R\,R which is bounded by the curve with equation y=2x+1y = \sqrt{2^x + 1}y=2x+1, the xxx-axis and the lines x=0x = 0x=0 and x=3x = 3x=3.
a.
[3]
Find k k\,k and complete the table below, giving values of 2x+1 \sqrt{2^x + 1}\,2x+1 to 3 decimal places.
| xxx | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
| 2x+1\sqrt{2^x + 1}2x+1 | 1.414 | 1.554 | kkk | 1.957 |
b.[4]
Use the trapezium rule to find an approximation, in terms of kkk, for the area of RRR.
c.[2]
State, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of RRR.
Integration Questions
864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.