XP Math Games Arcade

09-04-2007

Hi, I have a test tomorrow and I need to be able to Evaluate these integrals step by step.

1. $\int\frac{e^sqrt{x}}{sqrt{x}}dx$

2. $\int_{e}^{e^2}x^3ln(x)dx$

3. $\int\frac{x^2}{sqrt{16-x^2}}dx$

4. $\int\frac{2}{x^2+1}dx$

5. $\int\frac{x-2}{x^2-1}dx$

6. $\int\frac{x^2-1}{x-2}dx$

7. $\int tan^-^1(x)dx$

8. $\int sec^2(\theta)tan^2(\theta) d(\theta)$

thanks a lot, if you want you can email me the work and answers to alternet87@hotmail.com

09-04-2007

First: Are you a robot? If not, I'll help you.

09-05-2007

no I am not a robot. thanks. I might just pay someone to do these because I need to have them done soon, and I have no idea how. if you can do it before I pay someone that would be AWESOME !!!!! thanks

09-05-2007

If someone finishes the first set of problems for me, here are just a couple more questions that aren't AS important, but would be nice too.

1.) Consider the function $F(x)=\int_1^{e^x} \frac{2ln(t)}{t}dt$
a.) Compute the derivative $\frac{dF(x)}{dx}$ using the Second Fundamental Theorem of Calculus.
b.) Find F(0) and justify your answer showing work

2.) Suppose that $\int_1^x f(t) dt=x^2-2x+1$ Find F(x).

09-05-2007

I'll try one of the easy ones for warmup; I'll do the rest, if I can, later.

8) This is quite easy. You just break it into sections, and use the product rule.

$\int sec^2(\theta)tan^2(\theta) d(\theta)$

So, first work with
$\int\sec^2{\theta}$
Is equal to
$\int \ln{|sec{\theta}+\tan{\theta}|}^2 \text{ d}(\theta)$
as every good calc student knows. (Well, plus a constant, but we'll just stick that in at the end)
now, $\int\tan^2{\theta}\text{ d}(\theta)$ is equal to
$-\ln{|cos x|}^2$

Now apply the product rule
$\int f(x)\cdot g(x)=(\int f(x))g(x)+f(x)(\int g(x))$

I'll leave you to solve.

09-05-2007

i thought the product rule was only when finding the derivative, I need to find the anti-derivative. Maybe I am wrong but isn't $f'(x)$ the derivative of $f(x)$

The only thing I do know is that most of these problems can be solved by using Integration my substitution and Integration by Parts. I just don't know how to do it

09-05-2007

The same rule applies to integration. And yeah, oops, I'll fix that.

09-04-2007	#1
alternet87 Guest Posts: n/a	Integration... I need answers quick Hi, I have a test tomorrow and I need to be able to Evaluate these integrals step by step. 1. $\int\frac{e^sqrt{x}}{sqrt{x}}dx$ 2. $\int_{e}^{e^2}x^3ln(x)dx$ 3. $\int\frac{x^2}{sqrt{16-x^2}}dx$ 4. $\int\frac{2}{x^2+1}dx$ 5. $\int\frac{x-2}{x^2-1}dx$ 6. $\int\frac{x^2-1}{x-2}dx$ 7. $\int tan^-^1(x)dx$ 8. $\int sec^2(\theta)tan^2(\theta) d(\theta)$ thanks a lot, if you want you can email me the work and answers to alternet87@hotmail.com Last edited by Sillysidley; 09-04-2007 at 04:06 PM..

09-05-2007	#5
Temperal Guest Posts: n/a	I'll try one of the easy ones for warmup; I'll do the rest, if I can, later. 8) This is quite easy. You just break it into sections, and use the product rule. $\int sec^2(\theta)tan^2(\theta) d(\theta)$ So, first work with $\int\sec^2{\theta}$ Is equal to $\int \ln{\|sec{\theta}+\tan{\theta}\|}^2 \text{ d}(\theta)$ as every good calc student knows. (Well, plus a constant, but we'll just stick that in at the end) now, $\int\tan^2{\theta}\text{ d}(\theta)$ is equal to $-\ln{\|cos x\|}^2$ Now apply the product rule $\int f(x)\cdot g(x)=(\int f(x))g(x)+f(x)(\int g(x))$ I'll leave you to solve. Last edited by Temperal; 09-05-2007 at 08:33 PM..

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