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1. (a) Without using a calculator, determine the following integrals: 8.x dr3; (1) 2+8r- 9 (1)/ (ii) dr. r2 + 8x +41

1. (a) Without using a calculator, determine the following integrals: 8.x dr3; (1) 2+8r- 9 (1)/ (ii) dr. r2 + 8x +41

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. (a) Without using a calculator, determine the following integrals: 8.T dr. (ii) 2+8r+41 8r (1)/ r2 + 8x-9 (b) Let P(r, y) be a general point on the circle r + y? = 4 and let S be the point (2,0) as shown in the sketch below. P(r,y) Q(r, 0) S(2,0) (i) Write down expressions for r and y in terms of 0. Hence, show that the area A of the shaded region R is A = 20 – sin 20. (ii) Use Newton's method to determine the value of 6 (in radians, to three decimal places) such that A = 1. (Newton's method for solving (r) = 0: z,+1 = In f(In) for n = 0, 1, 2,...)
Transcribed Image Text:1. (a) Without using a calculator, determine the following integrals: 8.T dr. (ii) 2+8r+41 8r (1)/ r2 + 8x-9 (b) Let P(r, y) be a general point on the circle r + y? = 4 and let S be the point (2,0) as shown in the sketch below. P(r,y) Q(r, 0) S(2,0) (i) Write down expressions for r and y in terms of 0. Hence, show that the area A of the shaded region R is A = 20 – sin 20. (ii) Use Newton's method to determine the value of 6 (in radians, to three decimal places) such that A = 1. (Newton's method for solving (r) = 0: z,+1 = In f(In) for n = 0, 1, 2,...)
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