Question

Please help! Will FAN AND MEDAL!

Use two rectangles of equal width to estimate the area between the graph of f(x) = x − cos(πx) and the x-axis on the interval [1, 5]. Evaluate the function at the mid-point of each rectangle to find each height.

a. 8
b. 12
c. 16
d. 20

Answer 1

Can you please help? @mathmale @Nnesha @xGuardians

Answer 2

Alright, we can work on this one together, I gotcha :D

Answer 3

So first, what will our limits of integration be?

Answer 4

5 and 1

Answer 5

\[\int\limits_{1}^{5} x-\cos(pix)\]

Answer 6

Oh crap, I thought this was a volume question, disregard everything I said.

Answer 7

Well, not everything, first, how do we find the two midpoints between [1,5]?

Answer 8

Well I actually put that into my calculator and got 12. Which is one of the answers

Answer 9

That's not "estimating", so that's wrong.

Answer 10

I'll show you in a second why.

Answer 11

Dangit. I knew it seemed to easy to be true lol

Answer 12

So first, where will the two midpoints be between [1,5]? Do you know how to answer that?

Answer 13

no I do not

Answer 14

So you do 5+1 = 6, then divide by 2 to get the midpoint. I was wrong when I read it requires two rectangles, which means it only needs ONE midpoint, not two.
Therefore, 3 will be your midpoint

Answer 15

https://gyazo.com/5210b8d7e0b771a42f3578fbc83cfd89
So here, red is the area which would happen if you did not estimate.
Blue is the area that you get when you take the area in reference to rectangles.

Answer 16

https://gyazo.com/70637b33191f5b0d4e559546fc034394

Answer 17

That one ^

Answer 18

So if you were doing it without a calculator, you plug in the value 3 and see what f(3) =.

Answer 19

f(3) = 4

Answer 20

So now you know the Δx = 2 for the two rectangles, which we solved earlier.
The equation for the area is Δx*height
2 * 4 = 8
Then you have to double it since we have two rectangles of the same area.
16.
C

Answer 21

The height is found by f(3) = 4

Answer 22

Thank you. Can you help me with one more?

Answer 23

Can you make a new post, I hate scrolling down everytime when I jump around.