a) y = cos 2x on [0,1] b) x= on [1,10]

6)

a) $y=\cos \left(2x\right) on [0,\mathrm{\pi }]$

the length of the curve is given by 

$L={\int }_a^b\sqrt{(1+f\text{'}{\left(x\right)}^2)} dx$

here f(x)=cos(2x)

then f'(x)=-2sin(2x)

then the arc length is ${\int }_0^{\mathrm{\pi }}\sqrt{(1+(-2\sin {\left(2x\right))}^2} dx={\int }_0^{\mathrm{\pi }}\sqrt{(3-2\cos (4x\left)\right)} dx$=5.27