1.

By Simpson's rule, value of int_(1)^(2)(dx)/(x) dividing the interval (1,2) into four equal parts, is

Answer»

`0.6932`
`0.6753`
`0.6692`
`7.1324`

SOLUTION :`h=(2-1)/(4)=(1)/(4)`
Now, `x_(0)1, x_(1)=1+(1)/(4), x_(2)=1+2xx(1)/(4)`
`x_(3)=1+3xx(1)/(4),x_(4)=1+4xx(1)/(4)`
ie, `x_(0)=1, x_(1) =1.25, x_(2)= 1.5, x_(3)`
` =1.75, x_(4)=2`
`rArr y_(0)=1, y_(1)=0.8, y_(2)=0.667, y_(3)`
`=0.5571, y_(4)=0.5`
`:. ` Using simpson's `(1)/(3)` RD rule
`INT _(1)^(2)(dx)/(X)= (1)/(12)[(1+0.5)+4(0.8+0.571)+2(0..667)]`
`=(1)/(12)[1.5+5.484+1.334]`
`=(1)/(12) [8.318]=0.6932`


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