Compare the formula for mutiple trapezoidal rule n=3 versus the addition of 3 single trapezoidal rule for the same problem. compare the answer, will it be the same and why?
single trapezoidal rule :
fа) + f(6) 1- (6 — а) га) 2
multiple trapezoidal rule :
f(x)) f(x,) i (b-a)o) + (2 2n
example: f(x)=0.2+25x-200x2+675x3-900x4+400x 5
a=0 b=0.8

The chart shows the costs and shipping times for materials that a company needs to build a new product. which describes the best trade-off if the company needs to start building their product within the next two years? they should order the domestic materials because it is always best to choose the fastest shipping time. they should order the imported materials because it is always best to choose the lowest cost for materials. since the shipping time is longer, they should order the domestic materials because the additional cost is worth it to get the materials in time. even though the shipping time is longer, they should order the imported materials because they are less expensive and should arrive in plenty of time to build the product.