Which is longer from

x=2

to

x=4

: the curve

y=sec^(-1)x

or the curve

y=ln(2x^(3)+5x)

?\ Determine this by finding the length of each curve from

x=2

to

x=4

. 4 poms\

Are Lergth =\\\\int_a^b \\\\sqrt(1+[f^(')(x)]^(2))dx\ \\\\int_2^4 \\\\sqrt(1+[(1)/((x)(1-x))]^(2))dx\ \\\\int_2^4 \\\\sqrt(1+[(6x^(2)+5)/(2x^(3)+5x)]^(2))dx\ -2\ = ? \ =-1

12. Which is longer from x=2 to x=4 : the curve y=sec1x or the curve y=ln(2x3+5x) ? Determine this by finding the length of each curve from x=2 to x=4. 4 poms ArcLergth=ab1+[f(x)]2dx241+[x(1x)21]2dx241+[2x3+5x6x2+5]2dx