approximate the area under a curve using rectangles 😥

[regal temple]

for my calc class:

using the left-endpoint approximation to approximate the area under a curve of f(x) = 1 - (x/5) on thé interval [0,6] using n =3 rectangles. use exact value.

[thick mortar]

The best way to do this would be to draw out the function, in your case f(x) = 1 - (x/5), on your interval [0,6]. Then, draw vertical lines to split your function into three equally spaced rectangles (because n=3).

Since the problem wants left-sided endpoints, take the x values from the left side of each rectangle and plug each one, separately, into your function f(x) = 1 - (x/5) to get three new values.

This value is the height of that specific rectangle. So, the area of each rectangle is that value you got, multiplied by 2 (I got 2 because your interval is [0,6] which means it is 6 units long and n=3, so 6 units divided by 3 rectangles is 2 units per rectangle).

Once you have the area of each of these three different rectangles, you can add the three areas up for your approximation of the area under the curve.

[regal temple]

thank you for explaining !!!