Please be precise with the calculations

l. (a) Without using a calculator, determine the following integrals: . 8x .. 8:: (I) flame902\"\" (1') fmz+Sz+41d1 (13) Let P{z, y) be a general point on the circle 3:\" + y: = 4 and let S be the point (2, U) as shown in the sketch below. (i) Write down expressions for a: and y in terms of 6'. Hence, show that the area. A of the shaded region R is A=2Bsin2l9. (ii) Use Newton's method to determine the value of 9 (in radians. to three decimal places) such that A = 1. _ 1133!!) fTTnl ((4+ 4) + (6+ 6) = 20 marks) (Newton's method for solving f(:r:) = 0: In+1 = 1,, form = 0, 1,2, . . .)