*~*~*~*~*~* answers *~*~*~*~*~*
----------------------------------------------------------
| homework #1 | QSci 292 | |
| jjohnson@u |
---------------------------------------------------------------------------
1. Area under y = 1+3x^2 from x=0 to x=2 (note: x^2 means x raised to the power of 2)
1 square unit on the gragh = 5 rectangles (see units on the graph) hence, the area of a rectangle is 0.2 sq units number of rectangles inside the region = 42; lower limit of area = .2*42 = 8.4 number of border rectangles = 15; upper limit of area = .2*57 = 11.4 total number rectangles (inside+border)= 57; estimate of area (ave) = 9.9 sq units relative error: 1% [100(10-9.9)/10] %
trapezoid method
relative error: 2.5% [100(10.25-10)/10] %