Recent content by symmetric

Got the correction ! The modified solution is as follows - From above solution continuing up to step - g^{ij}\epsilon_{ipt}\epsilon_{jrs}\,=\, g^{ij}g_{ij} ( g_{pr}g_{ts} \, - \, g_{ps}g_{tr} ) \, - \, g^{ij}g_{ir} ( g_{pj}g_{ts} \, - \, g_{ps}g_{tj} ) \, + \, g^{ij}g_{is} (...

Homework Statement \mbox{Prove that}\,g^{ij} \epsilon_{ipt}\epsilon_{jrs}\,=\, g_{pr}g_{ts}\,-\,g_{ps}g_{tr} Notation : e_{ijk}\,=\,e^{ijk}\,=\,\left\{\begin{array}{cc}1,&\mbox{ if ijk is even permutation of integers 123...n }\\-1, & \mbox{if ijk is odd permutation of...

@vela @Hurkyl @tiny-tim Thanks for your reply. To clear confusion of variable 't' attaching original problem snapshot. From my understanding of given question it's distance traveled along circular path ( specifically for above problem ) . i] i generally don't use 't' for...

Homework Statement Consider path given by equation ( x - 1 )^2 + ( y - 1 ) ^2 = 1 that connect the points A = ( 0 , 1 ) and B = ( 1 , 0 ) in xy plane ( shown in image attached ). A bead falling under influence of gravity from a point A to point B along a curve is given by...

Method III - Using Green's theorem Given equation x^2 + z^2 = a^2 can be parametrized as follows - x = x z = \sqrt{ a^2 - x^2 } According to result obtained from Green's theorem we can write - Area = \int{ y ds }...

@lanedance You are right. After analyzing the problem again, posting the corrected area integral - Area integral = \int_{x = 0}^{ x = a } \int_{ y = a - \sqrt { a^2 - x^2 } }^{ y = a + \sqrt { a^2 - x^2 } }\frac{a}{ \sqrt{ a^2 - x^2 }} dy dx...

@lanedance - Thanks for your reply. You have pointed out correct typing mistake due to some 'copy paste'. Sorry for that. Corrected problem is as follows - 1. Homework Statement : Find surface area of part of cylinder x^2 + z^2 = a^2 that is inside the cylinder x^2 + y^2 = 2ay...

1. Homework Statement : Find surface area of part of cylinder x^2 + z^2 = 1 that is inside the cylinder x^2 + y^2 = 2ay and also in the positive octant ( x \geq 0, y \geq 0, z \geq 0 ). Assume a > 0. Homework Equations x^2 + z^2 = 1 x^2 + y^2 = 2ay ( x \geq 0...