Calculus Help

Test Preparation
1

<p>Hey</p>

<p>I just needed some help with some integration probs and would appreciate it if you could help me out:</p>

<p>1) find the integral of sin(e^(2x))cos(e^(2x))(e^(2x))
( find integral of sin times e raised to 2x times cos times e raised to 2x times e raised to the 2x ) </p>

<p>I got my answer to be -.5 cos (e^(2x) .. is this correct? </p>

<p>2) find integral of (sec^2(pi.x)) / (tan(pi.x) )..
I found this to be pi.ln(tan.pi.x) ? is this correct?</p>

<p>3) find area of 1-x^n. I am lost here since I do not know how to take the exponent into consideration when simplifying. I got x-ax^n-1</p>

<p>4) find integral of (sinx)/(3+cosx) ? would you make sinx=u and continue from there?</p>

<p>Thanks much..</p>

2

<p>nevermind.. I got the correct answers after some effort.. lol</p>

3

<p>do you know about chain rule integrals? chain rule makes some of the very simple, well at least the first one.</p>

4

<p>and to check if your answers are correct...</p>

<p>take the derivative of your answer, and you should get back what your original integrand was, or some equivalent form (sometimes w/ trig it may look different but it's equivalent)</p>

<p>if you don't get the original integrand, than it's wrong</p>

5

<p>
[quote]
do you know about chain rule integrals? chain rule makes some of the very simple, well at least the first one.

[/quote]
</p>

<p>Dont think I've learned that. Only learned u-substitution so far in addition to doing the integral in my head whenever possible.</p>

6

<p>use a TI-89. Thats what i do to figure it out.</p>

7

<p>well here's like the backwards chain rule... i hope i can make sense on line, it's fairly easy to explain in person...</p>

<p>we'll pretend this { is the integral sign...</p>

<p>say you had {f(x)f ' (x) dx</p>

<p>well then all you do is add one to the power for f(x) and divide by the new power...</p>

<p>for example in your first problem...</p>

<p>let f(x) equal sin(e^2x).... well f ' (x) equals cos(e^2x) times 2e^2x</p>

<p>well you have {f(x) f ' (x) except for the 2, so you just pull out a 1/2</p>

<p>thus, your answer is just .5(sin(e^2x))^2 all over 2. which also equals </p>

<p>.25 (sin(e^2x))^2</p>

<p>also for #4</p>

<p>let f(x) = (3 + cos x) ^ negative 1</p>

<p>then f ' (x) = negative sin x</p>

<p><strong><em>you only need the derivative of the inner part of the function, so you can ignore ^ negative</em></strong></p>

<p>so you must add a negative to the integrand, and put a negative on the outside</p>

<p>then your answer is</p>

<p>negative ln (3 + cos x)</p>

<p>and don't forget + C on everything!!</p>

<p>if that doesn't make sense and you're interested in learning it better, reply again and i'll try to explain it better</p>

8

<p>Hey... thats usually what I do.. except in the case of question 1, that didnt apply. It seems that I had to take U as e^(2x) only and not sin or cos. e^(2x) since its only of inner function.. This results in an answer of -cos(2.e^(2x))/8 which was confirmed by an online integral checker which I fuond. </p>

<p>Thanks much.</p>