OpenStudy (anonymous):

Use part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h(x)=∫ arctan 5t dt on the interval (4, 1/x). I got -5arctan(1/x)/x^2 but it was wrong

5 years ago
OpenStudy (anonymous):

well, when you take a derivative of an integral it should just be the function being integrated (arctan(5t)) evaluated at the upper bound (4)

5 years ago
OpenStudy (anonymous):

5 years ago
OpenStudy (anonymous):

From what I've been taught, the lower bound is insignificant when differentiating an integral.

5 years ago
OpenStudy (anonymous):

im sorry you 1/x is the upper bound isn't it. so it should be evaluated at that

5 years ago
OpenStudy (anonymous):

so it should be arctan(5/x)

5 years ago
OpenStudy (anonymous):

and do you put the 5 in front of that too?

5 years ago
OpenStudy (anonymous):

honestly, im a little unsure about this problem. In calc 4, we seem to treat the bottom bound as insignificant, but i did this problem on wolfram alpha and it gave: -arctan(5/x)/(x^2). So maybe im not the best one to be answering this. Sorry.

5 years ago
OpenStudy (anonymous):

actually, you are the best one to be answering it because it was correct! Thank you!!

5 years ago
OpenStudy (anonymous):

ok, great. like i said i just just used wolfram alpha. So im not really sure how to get to the answer the "correct" way. But maybe you can figure it out.

5 years ago
OpenStudy (anonymous):

well regardless thank you. I didn't know about the bottom bound being insignificant, so i'll keep that in mind!

5 years ago
OpenStudy (anonymous):

im not sure on this. but that may only be true if its a constant, not if its a function like x or something.

5 years ago
OpenStudy (anonymous):

ohh that would make sense

5 years ago
OpenStudy (anonymous):

you can check out http://mathmistakes.info/facts/CalculusFacts/learn/doi/doib.html for an example of how the bottom being a function affects things

5 years ago
OpenStudy (anonymous):

Thank you! That would be helpful

5 years ago
OpenStudy (anonymous):

No problem.

5 years ago