Assignment 4 Due : 4pm Monday 15 October MAS 182 Applied Mathematics Semester 2, 2012Mathematics and StatisticsPlease show all your working. Where possible give the exact answer./1 .,1 1. Consider the integral -12x + 3 dx. Using the trapezoidal method with n = 4 -i_ and n = 8, estimate the integral numerically. Calculate the integral exactly (using calculus and showing your working) and compare this with your numerical results. Find the following integrals. Show all working.(i) I (x2 + 3x — 1)e-2x dx (ii) I X-2 ln(3x) dx Find the average value of the function 1 mction f (s) = over s E [0, 2]. e3x A solid gold tip of a tunnelling electron microscope has the shape given by rotating the graph of the function f (x) = 3 — about the x-axis for s E [0, 9]. Find the volume of gold required to build the tip. Solve the following differential equations. Note that the solution may be either a general solution or a particular solution. )-.4 5 (ii) 4c1-3.1.d + 2xy — 3x = 0 with y(0) = 2 (iii) X dy (TT:. — 2xy + 5 = 0 with y(1) 3Notes:• 10% of the marks for this assignment are reserved for presentation. • There are penalties for late assignments. You must contact your tutor before the due date if you have difficulties making the deadline.1

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