Homework Statement
The sequence is 1 1 1 1 5 5 5 5 1 1 1 1
I need to find the formula for the sequence.
Homework Equations
The Attempt at a Solution
I had a previous problem that was similar. It was a sequence of 1 5 1 5 1 5. I managed to get it with the formula of...
Homework Statement
The problem is ∫e^x/(e^x)-1 to be evaluated from -1 to 1.
Homework Equations
The Attempt at a Solution
I got the integral as ln|(e^x)-1|
So, for the first part, evaluating from -1 to 0, with t being the limit at 0 I got this:
ln|(e^t)-1| -...
Homework Statement
Ok, this is a pretty simple integral, but I'm having trouble with the factoring.
\int \frac{1}{x^{2}+2}
According to the book, the answer is:
\frac{1}{\sqrt{2}} tan^{-1}(\frac{x}{\sqrt{2})}
Homework Equations
The Attempt at a Solution
So I need to get it in the form of...
Yes, I can integrate it from here, but since the problem is under the substitution review section in my book, I thought I would try to figure out how to do it with substitution.
I usually write the dx whenever I work my problems out on my official paper, but I do avoid it on my scratch work...
Ok, I was wrong again. I thought I had it figured out.
I have:
\begin{equation}\int 1 + e^{-x}\end{equation}
I set u = e^{-x} and du = -e^{-x} but then there is nothing for du to replace.
I'm lost again.
Ok, after reviewing it some more I found my problem. The derivative of e^{-x} is actually -e^{-x}. I didn't realize I had to bring down the negative sign.
And I did copy the answer wrong, it should be a -x exponent. My bad.
Thanks for the help.
Homework Statement
\begin{equation} \int \frac{e^{x}+1}{e^{x}}\end{equation}
Homework Equations
The Attempt at a Solution
This problem comes out of the substitution section of my book, and the answer in the back of the book is x-e^{x}+C
I started by changing the form to this...
Homework Statement
\begin{equation} \int_{-1}^{1} e^{u+1} \end{equation}
Homework Equations
The Attempt at a Solution
I really seem to struggle with any problems with e in them. I think I may have missed some of the basic rules or something, but I can't seem to find what I missed...
After looking through the book, I found a table of integrals that has the inverse sin function. I don't seem to have the inverse ones in my notes. I don't know how I missed that. I got it figured out now. Thanks for the help.
I don't think we have covered anything on arcsin yet. I'm only in Calculus 2. If I should know that at this level, I guess one of my teachers let me down.
6(1-t^{2})^{-1/2}
I tried to take the -1/2 exponent and add it to the 1-t^2 which gave me this:
= 6(1^{1/2}-t^{3/2}) = 6^{1/2}-6t^{3/2}
I figured I was doing it wrong, but my problem is that I'm not quite sure how to integrate 6(1-t^{2})^{-1/2}
I'm not really sure how to change it...
Homework Statement
[SIZE="5"]\int_{1/2}^{\sqrt{3}/2}\frac{6}{\sqrt{1-t^2}}dt
Homework Equations
The Attempt at a Solution
Ok, this is an odd problem I'm working from the book. The book says the answer is \pi.
First I tried getting rid of the fraction...