$(15$ points$)$ Problem $6.$ Biologist Bigelow counts the number of songbirds at a serious of elevations above the base of Pikes Peak. The following are Bigelow's results.

$\backslash$table$[[$Elevation $($m$),$songbirds$],[0,30],[100,60],[200,75],[350,90],[500,75],[700,60],[900,45],[1150,30],[1400,0]]$

What will Bigelow estimate the integral of these songbird numbers to be from the base of Pikes Peak to an elevation of $1400$ m if he numerically integrates the data

using the trapezoid rule with $8$ intervals: $0-100,100-200,200-350,350-500,500-700,700-900,900-1150,$ and $1150-1400?$

using the midpoint rule with $4$ intervals: $0-200,200-500,500-900,$ and $900-1400?$

using Simpson's rule with $4$ intervals: $0-200,200-500,500-900,$ and $900-1400?$