integration help

[synx]

if i had the problem x=1..0 int d/dx e^arctanx dx
will that have the same answer as x=1..0 d/dx int e^arctanx dx?

 

[stapel]

Your formatting is somewhat confusing. Are you inquiring about the potential equality of the following two expressions?

. . . . .\(\displaystyle \large{\int_1^0 \.\left(\frac{d}{dx}\, e^{\arctan{(x)}}\,\right)\,dx}\)

. . . . .$\displaystyle \large{\frac{d}{dx}\, \int_1^0\, e^{\arctan{(x)}} \,dx}$

When you reply, please include all of the work and reasoning you have tried thus far. Thank you.

Eliz.

 

[synx]

Yep, those questions, except the 0 on bottom and 1 on top of integral.

For the second one I believe the d/dx and integral cancel eachother out giving just arctan(x).

For the first, I'm not really sure if i'm doing it right, but I just did d/dx e^arctan(x) which is e^arctan(x)/x^2+1, then integrate that which brings back e^arctan(x) and do e^arctan(1) - e^arctan(0), which equals e^(pi/4) -1 .

 

[tkhunny]

For the second one I believe the d/dx and integral cancel eachother out giving just arctan(x).

Nice try. Think about it some more.

What is the value of the integral without considering the derivative?

What's the derivative of the answer to the previous question?