Question

Use inscribed rectangles to approximate the area under f(x) = –x2 + 7 for the –2 ≤ x ≤ 0 and rectangle width 0.5.

9.30 units2

9.75 units2

10.25 units2

10.75 units2

Answer 1

@phi

Answer 2

HI!!

Answer 3

Hey

Answer 4

this is going to take a lot of calculation

Answer 5

ok

Answer 6

first we need the endpoints of the intervals when we divide \([-2,0]\) in to pieces of length \(0.5\)

Answer 7

Ok would that be -2, -1.5, -0.5 and 0?

Answer 8

yes except you skipped one i think

Answer 9

-1

Answer 10

right

Answer 11

What do I do next?

Answer 12

ok next we see that it says "inscribed rectangles"
it is clear that on the interval \([-2,0]\) your function \(-x^2+7\) is going up (increasing)?

Answer 13

Yes?

Answer 14

lol it is a parabola that opens down with vertex at \((0,7)\) so it should be clear

Answer 15

ok

Answer 16

we need to know that so that we know the "inscribed rectangle" will use the left hand endpoints of your divided up intervals, not the right hand ones

Answer 17

So like on the negative side?

Answer 18

the interval you were given is \([-2,0]\) so yes, that is on the left of the graph, but that is not what i meant in the comment i just wrote
let me try to draw a picture