Calculus Problems

Jul 2010
4
0
Hi Everybody
I am new to this forum and thanks fo having me. I am still learning the rules for posting and will try not to infinge on any of the rules.
I am having a problem solving the ffg. 2 problems and would really like some assistance.

1.Find dy/dx if \(\displaystyle y=(sqrt x^2(1-sqrt x)/(1+sqrt x))\)

2. Find integral of \(\displaystyle dx/x(sqrt 4-(3lnx)^2)\)

Thanks in advance for all the assistance
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
This is very hard to read.

Are these what you were trying to write?

1. Find \(\displaystyle \frac{dy}{dx}\) if \(\displaystyle y = \frac{\sqrt{x^2(1 - \sqrt{x})}}{1 + \sqrt{x}}\)?

2. Find \(\displaystyle \int{\frac{dx}{x\sqrt{4 - (3\ln{x})^2}}}\)?


For 2.

\(\displaystyle \int{\frac{dx}{x\sqrt{4 - (3\ln{x})^2}}} = \frac{1}{3}\int{\left(\frac{1}{\sqrt{4 - (3\ln{x})^2}}\right)\left(\frac{3}{x}\right)\,dx}\).

Now let \(\displaystyle u = 3\ln{x}\) so that \(\displaystyle du = \frac{3}{x}\,dx\) and the integral becomes

\(\displaystyle \frac{1}{3}\int{\frac{1}{\sqrt{4 - u^2}}\,du}\).

Now try a substitution of \(\displaystyle u = 2\sin{\theta}\) so that \(\displaystyle du = 2\cos{\theta}\,d\theta\).