Math$102$

Q$1$: Find the length of the plane curve defined by the parametric equations

$x=e^{t}cost,y=e^{t}sint,0t1$

Q$2$: For the region bounded by the curve $y=4x^3$ and $x-$axis, $0x10,$ find

d$)$ The area of the region

b$)$ The volume of the solid generated by the region's revolution about the $x-$axis

c$)$ The area of the surface generated by revolution of the curve $y=4x^3$ about the $x-$axis

d$)$ The average value of the function $y=4x^3,0x10$