i stuck in this question please solve

1. (a) Evaluate the following integral: 3.r 10 - 7r+ 72 dr. (b) Let P(r, y) be a general point on the quartic polynomial y = r' and let Q be the point (3,0) as shown in the sketch below. P(x, y) Q(3. 0) (i) Write down an expression for the distance ( between P and Q in terms of r; (ii) Show that ( has a critical point at the value of a which satisfies the polynomial equation Ar' +r - 3 = 0; (iii) Without actually finding r, show that the solution of this equation lies in the interval [0. 3]: (iv) Show that ( is a (global) minimum at this a value. (v) Use Newton's method, with an initial guess of ro = 1.5 to find an approxi- mation (accurate to two decimal places) to the solution of Ar +r - 3 =0. (Newton's method for solving / (r) = 0: In+= In S(In) for " = 0, 1, 2, . ..)