The cross-section of a parabolic solar concentrator is modeled by the curve with equation
h=23x2+7,x≥0 h = \frac{2}{3}x^2 + 7, \quad x \ge 0 h=32x2+7,x≥0where h h\,h is the height in decimetres and x x\,x is the horizontal distance from the vertical axis. The concentrator is capped by a horizontal lid at h=31h = 31h=31. The finite region S S\,S is bounded by the curve, the hhh-axis (x=0x=0x=0), and the lid.
Find the exact area of the region SSS.
787 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.