Question 2 [3/3/4 marks] Compute the following integrals: (a) ((72 – 1)ec®-30 de (b) / 4+22+...
1) (30 pts) Compute the following indefinite integrals: le 12 de
do both
2. Evaluate the following integrals. (a) (7 marks) ( - In a de (b) (9 marki) | 5-14-1 de
3. 20 marks] Compute these integrals, with γ a circle of radius 2, Centre at origin, oriented counterclockwise: 2 2z (z-1)3, 22 42 γ ~2 + 8.
Question 9 (4 Marks) k4 Evaluate the following definite integrals: 2 k3 +36 9.1 S dk 9.2 S" (x® + e*) dx 9.3 %, (4x3 + 5x2 + 6x) dx (4 Marks) (7 Marks) [Sub Total 15 Marks]
Evaluate the following integrals. If the integral is divergent, state so. Make sure to clearly show all steps for full credit. (a) | 22 In zde (b) ſ sinº cosº o de (e) [ 74 - gyva dy (4 - y2)3/2 t •dt
Q.1 A. Compute each of the following integrals. 0 s V7(5x+3)+ te dv.(2 Marks) (1) Sax 24.dx. (3 Marks) B. (1) Evaluate dx. (3 Marks) (ii) Find the volume generated by revolving the curve y = sin x and y = 0 in 0 SXS ,about the x-axis.(2 Marks)
Question 4) (8 Marks) Given the following data: 0 1 4 -22 Flx) 30 28 12 Find f'(0),f (2),f'(4) and f"(0) with representations that are second order accurate (h2) and write a program/MATLAB script to compute the values.
Question 4) (8 Marks) Given the following data: 0 1 4 -22 Flx) 30 28 12 Find f'(0),f (2),f'(4) and f"(0) with representations that are second order accurate (h2) and write a program/MATLAB script to compute the values.
Exercise 12: Residues and real integrals (a) [6+4 points) Compute the residues for all isolated singularities of the following functions (i) f(2)== (2-) tan(2), (i) 9(2):= z2 sin () (b) (4+6+5 points) Compute (using the Residue theorem) (1) cos(72) ( d, A3 := {z € C:<3), 243 := {Z EC: | = 3}, 34, (2-1)(2 + 2)2(2-4) : 43 € C:21 <3}, po 12 To (x2 + 4)2 da, 24 2 + 4 cosat. J 5 + 4 sin(t)
please help with all parts of the question, thanks in
advance!
#5: Compute the following integrals for each of the cases R = 1, R = 5, R = 20 using as needed the facts in part # 4 a,b,c. Jx=R*** dz, Jx1=R (3-2)2-4) dz, S(x1=R 72-72 dz, Jx1=R (2–3)212–70)2 dz
1. (10 pts.) Compute the following integrals (a) [ 10 de In clos to (1) londo (a) seeds (bonus) 3+2V2)r? - 2x +3 dr (Hint: +1-(-x+ 2r - 1)(x - 2x - 1))