Let T: c'Ca, b →Clab] be given by and let TiC°[a,b]→C la, b] be givern ky Tz Cf GA)=S"fCt) dt for asxsb Funid the rube CT;T,) Cg Cx) a
Let T: c'Ca, b →Clab] be given by and let TiC°[a,b]→C la, b] be givern ky Tz Cf GA)=S"fCt) dt for asxsb Funid the rube CT;T,) Cg Cx) a
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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![Let \( T_1 : C^1[a, b] \to C^0[a, b] \) be given by
\[ T_1(f(x)) = f'(x) \]
and let
\( T_2 : C^0[a, b] \to C^1[a, b] \) be given by
\[ T_2(f(x)) = \int_a^x f(t) \, dt \quad \text{for} \, a \leq x \leq b \]
Find the rule \( (T_2 T_1)(g(x)) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe613d3f6-ed3c-4abe-81e0-270d8219b401%2F083da2e1-1c06-4a49-9062-329d0295afcd%2Ffwb3mp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( T_1 : C^1[a, b] \to C^0[a, b] \) be given by
\[ T_1(f(x)) = f'(x) \]
and let
\( T_2 : C^0[a, b] \to C^1[a, b] \) be given by
\[ T_2(f(x)) = \int_a^x f(t) \, dt \quad \text{for} \, a \leq x \leq b \]
Find the rule \( (T_2 T_1)(g(x)) \).
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