1. ## Integration Calculus Final

Hello everybody. I'm in sort of a bind here. For my calculus class we were given 60 integration problems with answers. Our job is to do the work from start to finish. My problem is I just so overwhelmed. We learn a new technique every class and I can't remember all the formulas and techniques to finish the problems.

Now I don't want straight answers, I really want to learn this stuff.

Here's an "easy" question from the final that I could not finish.

Problem:

$\displaystyle \int (\tan x + \text{cot}\, x)^2 \, dx$

$\displaystyle \tan x - \text{cot} \, x + C$

Looks easy enough, but for some reason I just can't make integration work for me. I don't know why the LaTex didn't work.

2. Originally Posted by LanceyPants
Hello everybody. I'm in sort of a bind here. For my calculus class we were given 60 integration problems with answers. Our job is to do the work from start to finish. My problem is I just so overwhelmed. We learn a new technique every class and I can't remember all the formulas and techniques to finish the problems.

Now I don't want straight answers, I really want to learn this stuff.

Here's an "easy" question from the final that I could not finish.

Problem:

$\displaystyle \int (\tan x + \cot x)^2 dx$

$\displaystyle \tan x - \cot x + C$

Looks easy enough, but for some reason I just can't make integration work for me.
Try $\displaystyle (\tan x + \cot x)^2 = \tan^2 x + 2 \tan x \cot x + \cot^2 x$

and use some trig. identites.

3. Originally Posted by danny arrigo
Try $\displaystyle (\tan x + \cot x)^2 = \tan^2 x + 2 \tan x \cot x + \cot^2 x$

and use some trig. identites.
So at least I'm not completely forgetful. I was able to get that far. All I know is the $\displaystyle \tan x \cot x$ cancel. Other than that I'm still stumped.

Here is another one that seems easy but I am just dumbfounded on.

$\displaystyle \int 10^{nx} \, dx$ The "n" and the "x" are supposed to be superscripted together.

4. $\displaystyle \int a^udu=\frac{a^u}{ln|a|}+C$

5. How do you all know so much about calculus? I study every day and nite and get no progress what so ever.

6. Study some more, and if that doesn't work out, then there must something wrong in your approach.

7. Originally Posted by LanceyPants
How do you all know so much about calculus? I study every day and nite and get no progress what so ever.
Some of us have been studying Calculus for years. For example, Soroban is a retired Math Professor.

8. Originally Posted by LanceyPants
How do you all know so much about calculus? I study every day and nite and get no progress what so ever.
I just started learning this stuff this semester. But I find the worst thing you can ever do for yourself is think something's too hard. Not like your brain will try to comprehend something you've already said it can't, right? Just don't get hung up and you'll be fine.

9. Oops, would probably help to answer that other question, huh? =p

tanx^2 + cotx^2 + 2
= (secx^2 - 1) + (cscx^2 - 1) + 2
= secx^2 + cscx^2

Now you've got two basic integrals

10. Originally Posted by derfleurer
I just started learning this stuff this semester. But I find the worst thing you can ever do for yourself is think something's too hard. Not like your brain will try to comprehend something you've already said it can't, right? Just don't get hung up and you'll be fine.
Well of course it's difficult, it's calculus. But for some reason when we started our study on integration, I just can't comprehend a dang thing.

But I just can't not hang up on this. There is too much riding on me to get an A. I need a perfect grade.

11. Originally Posted by LanceyPants
But I just can't not hang up on this...I need a perfect grade.

Most of what you do in calc isn't even calc. Remember that. All you're doing is playing with equations, getting them in a proper form, then performing integration or derivation after. It's more algebra and trig application than it is how to derive/integrate.

Check some online videos, they'll really help. Takes all the pressure off of you to have someone do the explaining for you for just a little while.

12. So it's come down to the fact that it's impossible for me to finish my final with a passing grade. I so want to curse down Calculus, but it's my fault for not having the intellectual capabilities to comprehend it.

13. Originally Posted by LanceyPants
So it's come down to the fact that it's impossible for me to finish my final with a passing grade. I so want to curse down Calculus, but it's my fault for not having the intellectual capabilities to comprehend it.
This thread is heading down a path that's best continued in the Chat Room.