more basic calculus

**turbod15b** · May 18th 2009, 10:07 AM

can some show me step by step please
thanks

**VonNemo19** · May 18th 2009, 10:15 AM

Show you what. I don' see anything. Are you talking about how you want someone to show you "Step-by-Step" the sitcom? I hated that show.

Nevermind, I can see it now.

**VonNemo19** · May 18th 2009, 10:17 AM

f) $\frac{1}{4}x^4+C$ The only step you need for this is the power rule. Do you know the power rule? Oh and algebra too. $dy=x^3dx\Longleftrightarrow\frac{dy}{dx}=x^3$

**VonNemo19** · May 18th 2009, 10:23 AM

Use the power rule for g too...........

$\frac{1}{3}x^3+x^2-3x+C$

You do know the power rule right?

**turbod15b** · May 19th 2009, 10:57 AM

thanks
but can u show me how to do it for all of them
thanks

**darthfader** · May 19th 2009, 11:43 AM

j) Let me do j for you step by step.

$\int{\frac{{x}}{{x^2 + 2}}}dx$

Let $u = x^2 + 2$
Then $du = 2xdx$

Notice that our $du$ is the same as the numerator of our given except of the numerical coefficient $2$ . Do you see it?

Now, we can put the $2$ by doing this.

$\frac{1}{2}\int{\frac{2xdx}{x^2+2}}$ Is this equal to the original given? Of course yes.

So we can continue.

Then
$\frac{1}{2}\int{\frac{2xdx}{x^2+2}} = \frac{1}{2}\int{\frac{du}{u}}$ .

There is a formula in integral calculus that states that the $\int{\frac{du}{u}} = \ln\left|u\right| + C$ .

Hence in our problem..

$\frac{1}{2}\int{\frac{2xdx}{x^2+2}} = \frac{1}{2}\int{\frac{du}{u}} = \frac{1}{2}\ln\left|u\right| + C$ .

Plugging in $u$ .

$\int{\frac{{x}}{{x^2 + 2}}}dx = \frac{1}{2}\ln\left|x^2 + 2\right| + C$

You can check by getting the derivative of our final answer. If it results to the given, then we're pretty much correct.

I hope this helps.

**turbod15b** · May 19th 2009, 11:46 AM

thanks bro
can u help me to the other 1s aswell
cheers

**darthfader** · May 19th 2009, 12:01 PM

For h, let me ask first, is it a Definite Integral? With limits 2 and 3? Do you know how to evaluate Definite Integrals?

The problem is quite easy and you can try it by yourself.

Try to continue this, just feel free to ask if you have some questions.

Hint: Start with this:

$2\int_2^3 {d\theta + } \frac{1}{2}\int_2^3 {\cos 2\theta (2d\theta )}$

**turbod15b** · May 19th 2009, 12:53 PM

im lost

**darthfader** · May 19th 2009, 07:24 PM

Can you tell me what part of solving the problem you find difficulties?

**VonNemo19** · May 19th 2009, 07:33 PM

Hey darth! If I were you, I would change my signature. You should write the work function so that it doesn't make you look like you don't know that the limit of a constant is that constant.

I'm just joking with you. Sometimes people can't pick up on humor through text.

The limit as x tends to infinity of work is, guess what?

MORE WORK! Get it?

**darthfader** · May 19th 2009, 10:35 PM

Thanks. I'll think about changing my signature. Maybe I can come up with a better one. Haha.

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