Question

The table below gives selected values for the function f(x). With 5 rectangles, using the left side of each rectangle to evaluate the height of each rectangle, estimate the value of the integral from 1 to 2 of f(x)dx.
x 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
f(x) 1 0.909 0.833 0.769 0.714 0.667 0.625 0.588 0.556 0.526 0.500

a) 0.7456 <----My answer, can you check if this is correct pls? Thanks
b) 0.6456
c) 0.6919
d) 0.6932

Answer 1

Again, because its difficult to understand the numbers on the top
x = 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0
f(x)=1, 0.909, 0.833, 0.769, 0.714, 0.667, 0.625, 0.588, 0.556, 0.526, 0.500

Answer 2

left hand [0.2] [ 1 + 0.833 + 0.714 + 0.625 + 0.556 ]
[0.2] [3.72] = 0.74

Answer 3

I get .7187

add row 2 from 1 to .526 and multiply by delta x = .1

Answer 4

okay but I am right with answer A, right?

Answer 5

well I got closer to .72

Answer 6

look, from 1 to 1.1 you use the left value of y which is 1
from 1.1 to 1.2 you use the left value of y which is .909
from 1.2 to 1.3 you use the left value of y which is .833
etc
there are ten of them and 10 * delta x = 1.0000

Answer 7

you never use the point ( 2.00, 0.500) because it is on the far right.

Answer 8

Draw it !

Answer 9

Oh, sorry, did not see use just 5 rectangles, you are right