How to solve these three question?

1.

(2 marks) Consider the integral 5 1= x20 (4-22 dx . For this kind of integral we usually use the substitution x = 2 sin 0 or x= 2cos0 x = 2sinh0 x = 2cosh0 ( x = 2tan0 O x = 2sec 0 Substituting x = 2 sin 0, assuming - 5 0 5 , leads to an integral of the form I = 2P sin' 0 . cost 0 de where P = ,m = 4 and n =(2 marks) Using the standard method, the integral / sin a cos a dac has the form sin' x cos xda = a17cos x + a16costx + a15cos x + a14cos x + a13cos 3x + a12cos 2x + ajjcos x + ajocos x + agcos x + C. Find this integral and enter the coefficents requested below. ag = a10= a11 = a12 = a13=(2 marks) You are given that 1 -12% dx = - 1 -12 + an-le-12x dx for n 2 1. 12 12 n 2e-120 da and enter your answer in the box below. Use this recurrence relation to calculate -12% dx =