Hi guys. I can't think of a way to start this integration - can someone set me on the proper path? Thanks!
What I have so far:
find the area of the surface obtained by rotating the curve around the x-axis
y=sin(pix), 0≤x≤1
dy/dx = picos(pix)
1 + (dy/dx)^2 = 1 + (pi^2)cos^2(pix)
integral 2(pi)sin(pix)√[1 + (pi^2)cos^2(pix)] = ?
If you are asking how to integrate
The answer is with relative difficulty. This one is really really ugly, from what i have seen. But you could always try trapezoid rule
The actual answer due to your specific definite integral is
EDIT: sorry I did not see the coefficient on the cosē, now I reevaluated it and it is too messy to type. but it is approximately 7.778
Hello, I appreciate the answer, but I was hoping someone could give me a hint on the mechanics. I'd like to solve this myself, but I've gone through several different processes and I'm still having problems. What sort of substitution am I looking at here?
Thanks,
swicket