Proof using FTC

  • #1

Homework Statement


Complete the proof by using the Fundamental Theorem of Calculus TWICE to establish
[tex] \int_c^d(\int_a^b f _{x}(x,y)dx)dy=...=\int_a^b(\int_{c}^{d}f_{x}(x,y) dy)dx [/tex]



Homework Equations


I know that the FTC states that if g(x)=\int_a^x(f), then g'=f


The Attempt at a Solution


I'm not sure how to use this fact to get the proof started. Any guidance would be appreciated.
 
Last edited:

Answers and Replies

  • #2
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Fixed your integral. You had [ \tex] rather than [ /tex].

Homework Statement


Complete the proof by using the Fundamental Theorem of Calculus TWICE to establish

[tex]
\int_c^d(\int_a^b f _{x}(x,y)dx)dy=...=\int_a^b(\int_{c}^{d}f_{x}(x,y)dy)dx
[/tex]



Homework Equations


I know that the FTC states that if g(x)=\int_a^x(f), then g'=f


The Attempt at a Solution


I'm not sure how to use this fact to get the proof started. Any guidance would be appreciated.
 

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