The profile of a decorative aluminum bracket is defined by the region RRR bounded by the vertical lines x=0x = 0x=0, x=10x = 10x=10, the xxx-axis, and the curve
y=15x+1 y = 15\sqrt{x + 1} y=15x+1All dimensions are given in centimetres.
By using a single trapezium extending across the full width of the region, calculate an approximation for the area of RRR. Provide your answer in cm2\text{cm}^2cm2 to two decimal places.
A set of 3 identical aluminum brackets is manufactured to this specification. Each bracket is cut from a sheet with a uniform thickness of 6 mm6\text{ mm}6 mm and the density of the aluminum used is 2.7 g/cm32.7\text{ g/cm}^32.7 g/cm3.
Use the trapezium rule with six ordinates (utilising the boundaries and four equally spaced internal points) to estimate the total mass of the 3 brackets combined. Give your answer to the nearest gram.
Without further calculation, state why the mass determined in part (b) could be: (i) an underestimate, (ii) an overestimate.
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.