Mass of a wire in shape of helix

syms x y z r t rho

x=cos(t*pi)

y=sin(t*pi)

z=8*t

r=[x,y,z]

rho=x^2+y^2+z^2

int(rho*norm(diff(r,t)),t,[0,1])

cos^2(x)+sin^2(x) should be equal to 1. As the problem above it not simply to 1. What are the way to simplify the answer by cos^2(pi*t)+sin^2(pi*t)= 1.

[Ganesh]

Have you tried out the Simplify function?

Answer 1

[Bjorn Gustavsson]

The symbolic tools make the default interpretation that all variables are complex. Therefore it cannot make that simplification.

If you explicitly constrain the variables to be real and use the simplify suggestion by@Ganesh you get:

syms x y z r t rho real
x=cos(t*pi)
y=sin(t*pi)
z=8*t 
r=[x,y,z]
rho=x^2+y^2+z^2
Lengthofhelix = simplify(int(rho*norm(diff(r,t)),t,[0,1]))

HTH