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Question 147
a.

Using the substitution u=3x+32sin⁡2xu = 3x + \frac{3}{2}\sin 2xu=3x+23​sin2x, show that

∫0π2e3x+32sin⁡2xcos⁡2x dx=16(e3π2−1) \int_0^{\frac{\pi}{2}} e^{3x + \frac{3}{2}\sin 2x} \cos^2 x \, dx = \frac{1}{6}(e^{\frac{3\pi}{2}} - 1) ∫02π​​e3x+23​sin2xcos2xdx=61​(e23π​−1)
[4]
b.

The design of a high-performance aerodynamic component involves a surface generated by rotating a region RRR through 2π2\pi2π radians about the xxx-axis. The region RRR is bounded by the curve with equation

y=18e32x+34sin⁡2xcos⁡x y = \sqrt{18} e^{\frac{3}{2}x + \frac{3}{4}\sin 2x} \cos x y=18​e23​x+43​sin2xcosx

and the coordinate axes in the first quadrant.

Use the result from part (a) to find the volume of the component, giving your answer in simplest form.

[3]

Integration Questions

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

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.

Question bank