Originally Posted by

**Grandad** Hello purplerainYou will have to set the question out more carefully if you want help here. I assume that this is an integration question (in which case it should be in the Calculus Form), but your use of notation is very unclear.

I can't see how you get $\displaystyle 4dt$. It's $\displaystyle \sin^2t + \cos^2t = 1$, not $\displaystyle -\sin^2t+\cos^2t$. And in any event, when you take the square root, you'll get $\displaystyle 2$, not $\displaystyle 4$.

The only way you can get $\displaystyle 4dt$ is if the expression is $\displaystyle \sqrt{(-4\sin t)^2+(4\cos t)^2}\;dt$. Is that what you mean?

The answer you quote, $\displaystyle \sqrt{32}$, suggests it may be a definite integral. Can we see the original question, please?

Grandad