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 dwC_D = \int_{\sqrt{2}}^{\sqrt{3}} \frac{12}{(4 - w^2)^{\frac{3}{2}}} \, dwCD=∫23(4−w2)2312dw
By using the substitution w=2sinθw = 2 \sin \thetaw=2sinθ, determine the exact value of CDC_DCD.
Practise Edexcel A Level Maths 11.5 Integration by Substitution with exam-style questions for A Level Maths. 59 questions, 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.