(b) Determine whether the following integrals converge. (i) ² x²+x-1 x5 + 3x dx, /2 5²1² ln(1+x²) x - X COS X dx. is the integral

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(b) ONLY

Determine whether the following integrals converge.
x²+x-1
x5 + 3x
dx,
(i) fº²
√²/²
(ii)
xx COS X
-
(c) For what values of a < B is the integral
So
(b)
کی
π/2 ln(1 + x²)
dx.
Ve-at-e-Bt
t dt
convergent?
Hint: start by taking the substitution u = e-t.
Show that
Transcribed Image Text:Determine whether the following integrals converge. x²+x-1 x5 + 3x dx, (i) fº² √²/² (ii) xx COS X - (c) For what values of a < B is the integral So (b) کی π/2 ln(1 + x²) dx. Ve-at-e-Bt t dt convergent? Hint: start by taking the substitution u = e-t. Show that
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