Find the first two iterations of the SOR method with ai = 1.1 for the following linear systems, using x<0 > = 0: a. c. 3A| - A2 + A3 = 1, 3A| + 6A2 + 2A3 = 0, 3AI + 3A2 4- 7A3 = 4. IOAI + 5A2 = 6, SAJ + 10A2 4x3 = 25, 4A2 + 8A3 A4 = 11, A3 + 5A4 = 11. b. IOai A2 =9. A| + 10x2 2X3 = 7, 2x2 + IOX3 = 6. d. 4xi + X2 + X3 + X5 = 6, X| 3x2 + A3 + X4 6, 2xi + X2 + 5x3 A4 X5 = 6, X| X2 X3 + 4X4 = 6, 2x2 A3 + X4 + 4x5 6

Integrals involving roots Let’s look at a couple of examples to see another technique that can be used on occasion to help with these integrals. Example 1 Evaluate the following integral. Solution Sometimes when faced with an integral that contains a root we can use the following substitution to simplify the integral into a form that can be easily worked with. So, instead of letting u be the stuff under the radical as we often did in Calculus I we let u be the whole radical. Now, there will be a little more work here since we will also need to know what x is so we can substitute in for that i