Finding the length of a parametric curve.
x=5sin^3t, y=5cos^3t, 0≤t≤pi
I've gotten the problem to this point:
15 Integral (sqrt(cos^2t*sin^2)dt
I'm not putting the bounds for convenience. I put this in the calculator and get 15, but I don't know how that happens. I know that's right because I also have the answer key, so there's that. But wouldn't what's in the integral simplify to sin t * cos t? Because it doesn't in the calculator, and that gives a different answer if you integrate that in the calculator. But it makes sense. Help?

Question

Finding the length of a parametric curve.
x=5sin^3t, y=5cos^3t, 0≤t≤pi
I've gotten the problem to this point:
15 Integral (sqrt(cos^2t*sin^2)dt
I'm not putting the bounds for convenience. I put this in the calculator and get 15, but I don't know how that happens. I know that's right because I also have the answer key, so there's that. But wouldn't what's in the integral simplify to sin t * cos t? Because it doesn't in the calculator, and that gives a different answer if you integrate that in the calculator. But it makes sense. Help?

anonymous · Answer

Basically, my question is what is
$$\sqrt{\sin^2(x)\cos^2(x)}$$
equal to, if it's not equal to
sin(x)cos(x)
Help would be the best.