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2. Find the values of p for which the integral converges and evaluate the integral for th dx a) dx b) c) x* In(: 0.

2. Find the values of p for which the integral converges and evaluate the integral for th dx a) dx b) c) x* In(: 0.

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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Number 2 (b,c)

d) e) (6x' +5)"* dx 2. 0 4+9x² f) 0. xIn x o Varctan x dx 1+x² 3x g) h) sec (3x)dx j) 2. Find the values of p for which the integral converges and evaluate the integral for those values of p. dx -dx 0 x (x* In(x)dx a) b) c) e 0. Check for convergence or divergence: 2x +3x +5 *+3'+2 dx x² +5* ∞ X+3* 1 dx x sin x 00 T/2 a) -dp- b) c) Ji 7x +9x' +2x 0. Tsin x dx 3 +5 +2" d) * xarctan x e) f) 0 5* +7* +2* (1 + x*} 3x +2* +5 dr 4x +3x+4 3x² +5x+4 J. 2x' +7x +1 h) i) =Ddx g) x'2" 7x° +2x +4 4. Find the arc - length of the following: 1 for 1<x<2 a) y = 8x2 e'+ b) y= In for 1<x<2 e* –1 c) x= arccos(1- y)+ V2y- y²; for -< y<1 x' + x* 1 ; for 0sxS2 +x + 3.
Transcribed Image Text:d) e) (6x' +5)"* dx 2. 0 4+9x² f) 0. xIn x o Varctan x dx 1+x² 3x g) h) sec (3x)dx j) 2. Find the values of p for which the integral converges and evaluate the integral for those values of p. dx -dx 0 x (x* In(x)dx a) b) c) e 0. Check for convergence or divergence: 2x +3x +5 *+3'+2 dx x² +5* ∞ X+3* 1 dx x sin x 00 T/2 a) -dp- b) c) Ji 7x +9x' +2x 0. Tsin x dx 3 +5 +2" d) * xarctan x e) f) 0 5* +7* +2* (1 + x*} 3x +2* +5 dr 4x +3x+4 3x² +5x+4 J. 2x' +7x +1 h) i) =Ddx g) x'2" 7x° +2x +4 4. Find the arc - length of the following: 1 for 1<x<2 a) y = 8x2 e'+ b) y= In for 1<x<2 e* –1 c) x= arccos(1- y)+ V2y- y²; for -< y<1 x' + x* 1 ; for 0sxS2 +x + 3.
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