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Integration: what variables can you move outside of the integrand? 
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#1
Jan2413, 04:29 PM

P: 273

[tex]1.\int { x } dx=x\int { 1 } dx\\ 2.\int { t } dx=t\int { 1 } dx\\ 3.\int _{ x }^{ x+1 }{ x } dt=x\int _{ x }^{ x+1 }{ 1 } dt[/tex]
Which of the equations are correct? 


#2
Jan2413, 05:09 PM

P: 1,474




#3
Jan2413, 07:00 PM

Mentor
P: 21,215

And 1 is incorrect. The following is a property of integrals:
##\int k~f(x)~dx = k\int f(x)~dx##, for k a constant, but there is no property that says you can move a variable across the integral sign. 


#4
Jan2413, 07:53 PM

P: 1,474

Integration: what variables can you move outside of the integrand?



#5
Jan2513, 09:16 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,339

You can move constants (and so variables that are independent of the variable of integration and so are treated like constants in the integration) outside the integral.
The integral on the left is [itex]x^2/2+ C[/itex] and on the right [itex]x(x+ c)= x^2+ cx[/itex]. 


#6
Jan2613, 11:52 AM

P: 273

Thanks for the clearup. :)



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