Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles. answer to the nearest integer.

43

Step-by-step explanation:

Estimate the area under the curve f(x) = 16 - x^2 from x = 0 to x = 3 by using three inscribed (under the curve) rectangles

First we find out the width of the rectangle

Δx=b−a/n,  a= 0 and b= 3, n= 3

so Δx= 1

Divide the interval [0,3] into  3 sub intervals of width=1

[0,1]     [1,2]     [2,3]

Now we plug in end point and evaluate the function

We take left endpoints

f(0) = 16 - 0^2=16

f(1) = 16 - 1^2= 15

f(2) = 16 - 2^2= 12

Now sum = Δx(f(0) + f(1)+f(2))

= 1 (16+15+12)= 43

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d