Surface Area of a Sphere | Lecture 40 | Vector Calculus for Engineers

Find the surface area of a sphere of radius R by computing a surface integral.

[malefetsanekoalane]

You sure don't miss a trick. You answer my questions before I ask them. Thanks a million.

[tpayne]

I've needed to see this solution from about 100 different angles, but it finally all clicks. Thanks a ton @Jeffrey!

[questionablemathematician]

Thank you for the time you put into your videos, they're excellent

[damnyutoobe]

Excellent. Complete derivation of the surface area

[noureldin]

Thanks, Prof Jeff, for valuable lecture.
for integral of d-Theta, =, why we take limits from zero to Bi only
Shall it from Zero to 2Bi as that is domain of moving Theta ?

[shashankgupta]

No comment!!! Ok you are doing a great job. Keep it up

[noureldin]

problem for lecture 40/ during integration, variable has been changed from SQRT(a^4/ab^2 + r^2) r dr to u^1/2
also limits from (0 to a) to (a^4/ab^2 to a^2+a^4/4b^2)
Kindly advise what is name of this conversion and how it done ?

[STKeTcH]

thanks man, finally a video for smart people! Why would you do it in any other way than

[lovejoymhishi]

why is theta going from zero to pi, ,, why isn't it going to 2pi ( Full revolution of the sphere to get the full surface )

[Festus]

CONFUSING BECAUSE, UNLIKE EVERY OTHER ONLINE VIDEO AND MATH TEXTBOOK, YOU HAVE SWAPPED THE FUNCTIONS FOR THETA AND PHI. VIRTUALLY EVERYONE USES PHI FOR THE ANGLE BETWEEN THE RADIUS (RHO) AND THE Z-AXIS.