In aerodynamic testing, the drag coefficient CDC_DCD of a specialized wing profile is modeled using the following definite integral related to the airflow pressure distribution:
CD=∫2312(4−w2)32 dw C_D = \int_{\sqrt{2}}^{\sqrt{3}} \frac{12}{(4 - w^2)^{\frac{3}{2}}} \, dw CD=∫23(4−w2)2312dwBy using the substitution w=2sinθw = 2 \sin \thetaw=2sinθ, determine the exact value of CDC_DCD.
Practise AQA A Level Maths 1.11 H: Integration with exam-style questions for A Level Maths. 436 questions covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
