My question is as follows: Let f (x) = (1+x)^(1/2) – (1-x)^(1/2). Find the Maclaurin series for f(x) and use it to find f ^5 (0) and f ^20 (0).
I got: X + Riemann Sum { [ (-1)^(n-1) 1x3x5**x(2n-3) ] / (2^n) x n！} X^n (after combining two Riemann Sums together). And I got (7！5！) / 16 5！ =...
Indeed, after what looked like endless calculation, I have finally got an answer: 12pi/5 (still learning this LaTex program). 2 0 ∫ 2pi 0∫1 [ r^4 (3/4 + 1/4 cos4θ ) + (1-r^2)^2 ] 1/(√1-r^2) r dr dθ. saltydog & rachmaninoff, thanks for your help!
Thanks saltydog. Then, I have 0 ∫ 2pi 0 ∫ 1 (r^4 + √ 1-r^2) (√1 + 4r^2) r dr dθ. Is this correct? If it is correct, any tips on how to solve this integration?
Here is the question:
Evaluate the surface integral ∫∫s (X^4 + Y^4 + Z^4) dσ, where dσ is the surface element and S = { (X,Y,Z) : X^2 + y^2 + Z^2 = 1}
I know you have to take the square root of 1 + (dz/dx)^2 + (dz/dy)^2 dxdy. And I got -2X/2Z and -2Y/2Z, respectively. Then, I must...