- Prove that L'es (Hint: By induction. Write esan) dx = 5-10 Rain) dx Break up the unit interval into 2-1 equal subintervals on each of which R₁-1 is constant. Show that 叮 x²] xpe x = ( ₁¹² + ~^²) * if J is one of these intervals.) - (²¹² + ²) [₁² e²S-1(x) dx

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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18. Prove that
S'essolo) dx
(Hint: By induction. Write
= (₁²+¹)*
2
dx =
L'eſfolk)
e²S,(x) dx = -fe
if J is one of these intervals.)
ets-(x)R(x) dx
Break up the unit interval into 21 equal subintervals on each of which
R₁-1 is constant. Show that
1₁ ²5. dx = (^² + e^") f₁c²
(~² + €¯)¸
e²S-1(x) dx
Transcribed Image Text:18. Prove that S'essolo) dx (Hint: By induction. Write = (₁²+¹)* 2 dx = L'eſfolk) e²S,(x) dx = -fe if J is one of these intervals.) ets-(x)R(x) dx Break up the unit interval into 21 equal subintervals on each of which R₁-1 is constant. Show that 1₁ ²5. dx = (^² + e^") f₁c² (~² + €¯)¸ e²S-1(x) dx
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