MAST10006 Calculus 2, Summer Semester, 2021 Assignment 3 School of Mathematics and Statistics, The University of Melbourne • Submit your assignment solutions online in Gradescope (link available on LMS) before midnight 31 January 2021 • Submit your solutions as a single PDF file with the pages in the right order and correct orientation. You may be penalised a mark if you do not. • This assignment is worth 5% of your final MAST10006 mark. • Marks may be awarded for: ◦ Correct use of appropriate mathematical techniques ◦ Accuracy and validity of any calculations or algebraic manipulations ◦ Clear justification or explanation of techniques and rules used ◦ Use of correct mathematical notation and terminology • You must use methods taught in MAST10006 Calculus 2 to solve the assignment questions. 1. Evaluate the following integrals: (a) ∫ 2 x(x + 1)(x2 + 1) dx (b) ∫ x2e2x dx. 2. Solve the first order ODE: dy dx = tanh 2 3y cosh2y x2 (x 6= 0). 3. (NOT to be assessed) Evaluate ∫ 1 e x 2 + e x 3 + e x 6 + 1 dx [End of assignment] 欢迎咨询51作业君