Please answer the questions, so I can check with the ones I handed in.

Question 4 (16 marks) a. Find the following integrals: (2 marks) dx i. J 4x+4 (3 marks) ii. Just (t2 - 5)dt x dx, using the substitution u = 4 - x2. (3 marks) iii. J V 4 - x2 b. Consider the curve defined by the equation y3 = 6xy - x3. i. Use implicit differentiation to find - in terms of x and y . Use your result to dx show that the gradient of the tangent to the curve at the point (3,3) is -1. (5 marks) ii. Determine the equation of the tangent to this curve at the point (3,3) and find the point where this tangent intersects the y axis.