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TrueTears · « **Reply #375 on:** June 13, 2009, 02:01:10 am »

Think you did it for rotated around x axis

but I got it now, thank you kamil!

TrueTears · « **Reply #376 on:** June 13, 2009, 02:59:55 pm »

If $\frac{dy}{dx} = \sqrt{sinx}$ and y = 1 when $x = 0$ , then the value of y when $x = \frac{\pi}{3}$ can be found by evaluating?

Show all working.

Thanks.

Winston · « **Reply #377 on:** June 13, 2009, 03:05:50 pm »

Hey Truetears. Which program do you use to write your equations with?
Cheers

TrueTears · « **Reply #378 on:** June 13, 2009, 03:13:20 pm »

http://vcenotes.com/forum/index.php/topic,10280.0.html

Winston · « **Reply #379 on:** June 13, 2009, 03:17:36 pm »

thanks

Damo17 · « **Reply #380 on:** June 13, 2009, 03:21:51 pm »

Quote from: TrueTears on June 13, 2009, 02:59:55 pm

If $\frac{dy}{dx} = \sqrt{sinx}$ and y = 1 when $x = 0$ , then the value of y when $x = \frac{\pi}{3}$ can be found by evaluating?

Show all working.

Thanks.

NOTE: taking a stab at this.

$\frac{dy}{dx}= \sqrt{sinx}$

$\int \sqrt{sinx}= \int (sinx)^{\frac{1}{2}}= -\frac{cos^{\frac{3}{2}}x}{\frac{3}{2}} +c$
$= -\frac{2cos^{\frac{3}{2}}x}{3} +c$

$y=1$ when $x=0$

$1=-\frac{2cos^{\frac{3}{2}}0}{3} +c$
$1=-\frac{2}{3} +c$
$c=\frac{5}{3}$

when $x=\frac{\pi}{3}$

$y= -\frac{2cos^{\frac{3}{2}}(\frac{\pi}{3})}{3} + \frac{5}{3}$
$y=-\frac{2(\frac{\sqrt{2}}{4})}{3}+\frac{5}{3}$
$y=-\frac{\sqrt{2}}{6}+\frac{10}{6}$
$y=\frac{10-\sqrt{2}}{6}$

TrueTears · « **Reply #381 on:** June 13, 2009, 03:35:27 pm »

Thanks for having a go but I don't think $\sqrt{sin(x)}$ is integrable XD

I'm looking for more of an expression which can be used to evaluate it. (If you know what I mean lols)

Damo17 · « **Reply #382 on:** June 13, 2009, 03:46:21 pm »

Quote from: TrueTears on June 13, 2009, 03:35:27 pm

Thanks for having a go but I don't think $\sqrt{sin(x)}$ is integrable XD

I'm looking for more of an expression which can be used to evaluate it. (If you know what I mean lols)

Just thought I would give it a go.

Just curious as to where you got this question?

TrueTears · « **Reply #383 on:** June 13, 2009, 04:03:41 pm »

NEAP topic test.

Damo17 · « **Reply #384 on:** June 13, 2009, 04:04:22 pm »

Quote from: TrueTears on June 13, 2009, 04:03:41 pm

NEAP topic test.

Do you have the answer?

TrueTears · « **Reply #385 on:** June 13, 2009, 04:06:53 pm »

No answers sorry

Damo17 · « **Reply #386 on:** June 13, 2009, 04:12:39 pm »

Have a look here:

http://www.physicsforums.com/archive/index.php/t-8259.html%253Cbr%2520/t-83012.html
http://en.wikipedia.org/wiki/Elliptic_integral

ed_saifa · « **Reply #387 on:** June 13, 2009, 04:14:08 pm »

Maybe this question requires Euler?

Damo17 · « **Reply #388 on:** June 13, 2009, 04:39:37 pm »

this questions looks like it can be done only by calculator (in the spesh course).

From calc:
$fnInt(\sqrt{sinx},x,0,\frac{\pi}{3}) = 0.94$

TrueTears · « **Reply #389 on:** June 13, 2009, 04:46:26 pm »

Alright cool thanks guys.

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