2 times the integral from 0 to 1 of (2t-3t^2) *sqrt(1-9t^2) dt.

Thank you very much.

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- November 3rd 2007, 08:10 AMkittycatintegration - urgent help please
2 times the integral from 0 to 1 of (2t-3t^2) *sqrt(1-9t^2) dt.

Thank you very much. - November 3rd 2007, 08:25 AMtopsquark

First let's get that radicand simplified a bit:

Let

The first integral may be done using a simple substitution. I'll let you deal with that. For the second integral:

Take a moment and look at the graph I've posted below. You can easily see that this integrand does not exist beyond x = 1. So

<-- We need to do this, else the substitution below is illegal.

Now Let

I'll let you do this one also and then collect all the pieces.

-Dan - November 3rd 2007, 08:48 AMSoroban
Hello, kittycat!

A variation on Dan's solution . . .

Quote:

. . and: .

Substitute: .

. .

For the first integral, use:

For the second integral, we have:

. .

Can you finish it?

- November 3rd 2007, 08:55 AMtopsquark
- November 3rd 2007, 09:21 AMkittycat
what about for this integral,

the integral of t^2 *sqrt(1+9t^2) dt. How should I solve it? Thank you very much. - November 3rd 2007, 09:30 AMtopsquark
- November 3rd 2007, 09:46 AMkittycat
Quote:

Originally Posted by**kittycat**http://www.mathhelpforum.com/math-he...s/viewpost.gif

*what about for this integral,*

the integral of t^2 *sqrt(1+9t^2) dt. How should I solve it? Thank you very much.

Instead of using the sine function, use the tangent function. (http://www.mathhelpforum.com/math-he...632bea41-1.gif.)

-Dan

Hi Dan,

Could you please show me how to let the tangent function in this question? Sorry to ask you because I forgot the trig substitution. Thank you very much. - November 3rd 2007, 09:56 AMtopsquark
- November 3rd 2007, 07:29 PMkittycathelp me again please
http://www.mathhelpforum.com/math-he...256dda3d-1.gif

Hi,

I might be wrong in the process of calculation. :(But don't know why can't get the answer (given by the textbook) from your approach.

The answer given by the textbook is -11/108 *sqrt(10) -1/36*ln(sqrt(10)-3) -4/27

help me again please:D - November 4th 2007, 02:00 AMtopsquark
- November 4th 2007, 08:15 AMkittycat
he same way that Soroban did, though in this case there are no restrictions due to the limits. So

http://www.mathhelpforum.com/math-he...4654d32f-1.gif

Let http://www.mathhelpforum.com/math-he...1814665f-1.gif

So

http://www.mathhelpforum.com/math-he...ae7cc688-1.gif

http://www.mathhelpforum.com/math-he...ab7e230e-1.gif

========================

*Referring to : the integral from 0 to 1 of t^2 *sqrt(1+9t^2) dt.*

I got to the same answer as you posted. But how should i evaluate it if it is =>*the integral from 0 to 1 of t^2 *sqrt(1+9t^2) dt.*

Could you please guide me to the final answer of this integration?

Thank you very much. (Handshake)