Net Change Theorem

[lovetolearn]

The numbers connected by the ___ line are above or below the integral sign or the bracket.


Evaluate the integral


1
∫ (d/dx)(e^arctanx)dx
0


My work:


1_____________________________1
∫ (d/dx)(e^arctanx)dx=[e^arctanx] =e^(pi/4)-1 by the net change theorem, is that correct?
0_____________________________0

 

[Deleted member 4993]

The numbers connected by the ___ line are above or below the integral sign or the bracket.


Evaluate the integral


1
∫ (d/dx)(e^arctanx)dx
0


My work:


1_____________________________1
∫ (d/dx)(e^arctanx)dx=[e^arctanx] =e^(pi/4)-1 by the net change theorem, is that correct? Yes ... as noted below I did not notice the d/dx at the front
0_____________________________0

start with substitution

u = arctan(x) → dx = sec²(u) du

Now continue......

 

[HallsofIvy]

Yes, that is correct. I suspect that Suhotosh Khan misread the problem, perhaps not seeing the "d/dx".

 

[lovetolearn]

Thank you!