Good morning, I'm hesitating with the following exercise:

Let [tex]\sigma[/tex] be the path:

[tex]x=\cos^{60}t, \;\;\;\;y=\sin^{60}t,\;\;\;\;z=t, \;\;\;\;0 \le t \le \frac{59 \pi}{2}[/tex]

Evaluate the integral

[tex]\int_{\sigma}\sin^{58}z\;dx+\cos^{58}z\;dy+(x^2y^2)^{\frac{1}{60}}dz[/tex]

So that's the statement. Now, what I've done is changing the variables:

[tex]\mathrm{d}x=-60\sin t\cos^{59}t\, \mathrm{d}t[/tex]

for the three x, y and z. Then the integral becomes

[tex]\int^{59π/2}_{0}−60\cos^{59}t\sin^{59}tdt+\int^{59π/2}_{0}60\sin^{59}t\cos^{59}tdt+\int^{59π/2}_{0}\cos^2t\sin^2tdt[/tex]

Is that procedure correct? I mean, would the solution to the sum of the three integrals be the solution of the first integral with [tex]\sigma[/tex]?

Thanks in advance