You have an unknown function that is monotone increasing for 1<x<5 and have the following information about the function values. With the clear understanding that there is no way to get an exact integral, how would you try and approximate the area under the curve?

Question

X=(1, 1.2, 1.6, 2.8, 2.9, 3.3, 3.6, 4, 4.2, 4.8, 5)
Y = (3.170, 3.505, 4.317, 8.516, 9.041, 11.528, 13.885, 17.873, 20.312, 29.982, 32.724)

Answer 1

area= sum y*deltax

start at x=1, make a table
deltax yavg
.2 (6.675/2=?)
.4 (3.505+4.317)/2
and so on, then add the products of yavg*dx