Question

5 The shape of a new discus is being studied at the Institute of Aeronautics. A young scientist is convinced that if the discus has a cross-sectional shape of the form f(x) =22 for x e b, bl, where a and b are real numbers, then the resulting shape formed as a volume of revolution will have a reduced air drag and hence travel further when thrown by an athlete. a +x a Sketch a graph of f(x):[b, b] -R where f(x) = --and shade in the area bounded by f(x), the x-axis, xb and x b. b One of the designs being investigated has a=3 cm and b =5 cm. Calculate the shaded a area. c Write, but do not attempt to solve, the integral that determines the volume of the discus. Hint: Use the symmetry of fix) about the y-axis to write the integral whose limits of integration are x=0 and 5 d The integral in part c gives the volume of the discus. Use a graphics or CAS calculator to 637 calculate the volume of the discus. CHAPTER 6 In

Integral calculus, show your working clearly please

Answer 1

f(x) Eb,b Rb a ar tx2 Ya -b (0,0) at 3, 6 5 3 R by t(x) 9+ X2 E5 O333 -5 010,0) 5T -5 3. tan tau 376 +1.03 0376 1 2.0607