Assignment 8

Problem #6:

y =   ____ Ö4x+4           0 £ x £ 8

y = 2   ___ Öx+1

y¢ = (x+1)[(-1)/2]

S = 2 p ó õ 8 0  2   ___ Öx+1   Ö   1+(y¢)2   dx = 4 p ó õ 8 0    ___ Öx+1   Ö   1+((x+1)[(-1)/2])2   dx

S = 4 p ó õ 8 0    ___ Öx+1     æ  ú Ö 1+ 1 x+1   dx = 4 p ó õ 8 0    _____ Öx+1+1   dx

S = 4 p ó õ 8 0    ___ Öx+2   dx = é ê ë 4 p 2 3 (x+2)[3/2] ù ú û 8 0

S = [(8 p)/3] ( 10^[3/2] - 2^[3/2] ) » 241.23

Problem #22:

S = 2 p ó õ [(p)/4] 0  tan(x) Ö   1 + sec4(x)   dx

Note that the integrand is not simply tan(x), but tan(x)Ö{1 +sec⁴(x)}. Also note that I've pulled out the factor of 2 p:

S = 2 p p 120 é ê ë 1 ·f(0) + 4 ·f( p 40 ) + 2 ·f( 2 p 40 ) + ¼+ 2 ·f( 8 p 40 ) + 4 ·f( 9 p 40 ) + 1 ·f( p 4 ) ù ú û

S₁₀ » 3.84