Question

Using n = 4 equal-width rectangles, approximate the integral from negative 2 to 2 of the quantity x squared plus 8, dx. Use the left end-point of each sub-interval to determine the height of each rectangle.

Answer 1

so you have this integral right?

\[\Large \int_{-2}^{2}(x^2+8)dx\]

Answer 2

yes

Answer 3

ok thanks

Answer 4

were you able to get the graph set up for this?

Answer 5

if not, I can show you if you want?

Answer 6

i dont know how

Answer 7

ok the first step is to just graph f(x) all by itself. I'm using geogebra to do so

Answer 8

we are given n = 4, a = -2 and b = 2

so

\[\Large \Delta x = \frac{b-a}{n}\]

\[\Large \Delta x = \frac{2 - (-2)}{4}\]

\[\Large \Delta x = 1\]

agreed?

Answer 9

yes

Answer 10

so what we do is start at a = -2 and count up by delta x units (ie count up by 1) until we hit b = 2

Answer 11

so we have: -2, -1, 0, 1, 2

those will be x values to be plugged into the f(x) function

Answer 12

for example,

x = -2

f(x) = x^2 + 8
f(-2) = (-2)^2 + 8
f(-2) = 12

so the point (-2,12) is on the graph. Do the same for the other x values and you'll get these points

Answer 13

the points A through D will determine the heights of the rectangles. The y coordinates of the points specifically

Answer 14

(-2+8)+(-1+8)+(0+8)+(1+8)+(2+8)=40

Answer 15

do you see in my last attached image how I set up the rectangles?

Answer 16

yes i just saw it

Answer 17

find the area of each rectangle, then add up the areas

Answer 18

k

Answer 19

12+9+8+9=38

Answer 20

correct

Answer 21

Awesome than you so much.

Answer 22

you're welcome