Recent content by mahdisadjadi

After 1 month work on this problem, I found out following remarks: 1. If we tend to use "Brioschi formula" to calculate Gaussian curvature of a surface, we should embed it into a 2D space. For example, in the given metric, we should take r=constant to achieve a surface in theta-phi 2D space...

@ HallsofIvy Thanks!:smile:

Rewrite the power as: -x^{2}+2x=-(x-1)^2+1 It we define x-1=t, -x^{2}+2x=-t^2+1 so e^{-x^{2}+2x}=e^{-t^2+1}=e^{-t^2}e^{1} and we also know that dx=dt, change the variable of integral and enjoy!

Well, f(x)=x(x^{3}+2x)^{\frac{1}{2}} If we apply the product rule, we should write: \frac{df(x)}{dx}=(\frac{dx}{dx})[(x^{3}+2x)^{\frac{1}{2}}]+x(\frac{d[(x^{3}+2x)^{\frac{1}{2}}]}{dx}) So if we rearrange the equations...

Yes, your answer is correct: A=\frac{1}{2}\int\limits_{0}^{\frac{\pi}{3}} [sin(3\theta)]^{2} d\theta = \frac{\pi}{12}

[FONT="Georgia"][FONT="Tahoma"]Homework Statement Assume that we have a metric like: ds^{2}=f dr^{2}+ g d\theta^{2}+ h d\varphi^{2} where r,\theta , \varphi are spherical coordinates. f,g and h are some functions of r and theta but not phi. Homework Equations How can I calculate...