\The figure shows a sketch of the cross-section of a custom-engineered support beam, bounded by the curves C1C_1C1 and C2C_2C2 with equations\C1:y=x3−6x2+5x+12,x≥0C_1 : y = x^3 - 6x^2 + 5x + 12, \quad x \ge 0C1:y=x3−6x2+5x+12,x≥0\C2:y=−x2+3x+4,x≥0C_2 : y = -x^2 + 3x + 4, \quad x \ge 0C2:y=−x2+3x+4,x≥0\The curves C1C_1C1 and C2C_2C2 intersect at the points AAA and BBB as shown in the figure. Point AAA has coordinates (2,6)(2, 6)(2,6).\Using algebra and showing all steps of your working,
find the coordinates of the point BBB.
The finite region RRR, shown shaded in the figure, is the cross-sectional area enclosed between C1C_1C1 and C2C_2C2.\Use algebraic integration to find the exact area of RRR.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
