How to find in differentiation in area and volume?

QUESTION 3 a) The Mean Value Theorem for differentiation states that if f(x) is differentiable on (a,b) and continuous on [a,b], then there is at least one point c in (a,b) where f (c)=_(b) -f(a) b- a If f (x) =3x2 - x3 , find the value of c in the interval (1,3) that satisfies the above theorem. (4 marks) b) Evaluate (x + 1) (x2-4x+3) dx (3 marks) c) Evaluate each of the following integrals using the appropriate substitution. i) -6x2 13-4x -dx (4 marks) cos ec (2x) 4- cot(2x) dx (4 marks) d) Find the value of k it k (1+ x) dx+ (2k - x2)ox - -4 (4 marks)QUESTION 4 a) Figure 1 below shows the region W bounded by the curve y = vx + 4 and the line x = 5. V = Vx+4 W Figure 1 i) Find the area of the shaded region W. (4 marks) ii) Find the volume of the solid generated when the shaded region W is revolved about the x-axis using the Disk Method. (5 marks) b) Figure 2 below shows the region R bounded by the curve y = x -4x and the line y = -x. y = x - 4x (0.0) (3.-3) Figure 2 Find the volume of the solid generated when the shaded region R is revolved about the y = 0using the Washer Method.