Question 4 10 marks You should be able to answer this question after studying Unit 8. (a) Use integration by substitution to find this indefinite integral / 6x% + 4z + 2 d B+' +z (b) Use integration by substitution to evaluate this definite integral, giving your answer in exact form '/{]% sec?(z)(tan(z) + 3)*dz. Question 5 10 marks You should be able to answer this question after studying Unit 8. This question is about the function f(0) = (20 3) cos(20). (a) Explain why the graph of f lies on or above the #-axis for all values of in the interval [3T, 2T]. (b) Write down an expression, involving a definite integral, that gives the area between the graph of f and the f#-axis, from 6 = C'% to O = %. (c) Use integration by parts to find the area described in part (b), giving the exact answer. Question 6 10 marks You should be able to answer this question after studying Unit 8. (a) Use integration by substitution to find the indefinite integral /e\"'(ew 5)(1 + 2%)%dx. (b) Use integration by parts twice to find the indefinite integral / (y* + 3y) sin(y)dy. [4] [6] [3] [1] [6] [5] [5]