Question

Calculus Question!! Medal!!

Answer 1

@rebeccaxhawaii

Answer 2

dunno that one myself

Answer 3

The integral is the same at the area under the curve. So given the integral from -2 to 2, the width of each of the 4 rectangles are \[\frac{ 2-(-2) }{ 4 }=1\]
Since this is a midpoint sum, you need to to find the midway point of each rectangle, which would be at the .5 mark.
You plug in each x-point, which are -1.5,-0.5,0.5, 1.5, to find their respective y values.
To find the area of each rectangle you multiply the width (1) by the height (y).
You then add all the rectangles together to get your Mid-point sum.

Answer 4

Ohhh wow I understand now.

Answer 5

ok so where do I plug in -1.5,-0.5,0.5, 1.5

Answer 6

Into the equation x^3 +8

Answer 7

and then I solve that and multiply it by 1 and then add them all up?

Answer 8

Yes! It is just 1, because that just so happens to be the width. Normally you would multiply it by some other number.

Answer 9

So do i plug them in to just x^3+8 or the whole \[\int\limits_{-2}^{2} (x^3 +8) dx\]

Answer 10

Just x^3+8 because the integral is just the equation for finding the area under the curve.

Answer 11

ok let me do that. i can't message you when I've done it if you want?

Answer 12

Yeah! I would love to see what you get!

Answer 13

ok cool i'm almost done

Answer 14

I got about 32.015

Answer 15

I got exactly 32

Answer 16

\[[1*[(-1.5)^3+8]] +[1*[(.5)^3+8]]+[1*[(.5)^3+8]]+[1*[(1.5)^3+8]]\]

Answer 17

The first .5 should be negative.

Answer 18

that's exactly what i did. I guess using the rectangle method is never exactly accurate. Anyway is 32 the final answer?

Answer 19

Yes. I did that and got exactly 32.

Answer 20

That fine I agree I just wanted to know if there are any more steps or if 32 is the final answer?

Answer 21

I just meant it was the final answer.

Answer 22

oh okay. Thanks for the help :)

Answer 23

No problem!