Find the area under the curve of y=-2x+6 from x=0 to x=3 using 3 strips of equal length using right endpoints.
I tried this equation before and my answer was 9 but my teacher said it was wrong? and I also posted this before and Someone who helped me got the same answer. So I'm very confused
widths: x 0 to 1, 1 to 2, 2 to 3
right endpoints, x=1,2,3
area=height*width=(-2+6)1 + (-4+6)1 + (-6+6)1=4+2+0
check my thinking.
Maya, I looked at your last tutors (Dr Reiny), and his answer assumed the estimation using trapazaoids, which is a better estimate of this curve. I did above assuming rectangle strips, right end points, which will underestimate the area. My guess is your teacher wants you to use the simple rectanular strips, error prone as it is.
Calculus - Reiny, Friday, June 17, 2016 at 7:25am
Your 3 strips would be 3 trapezoids.
The confusing part is the fact that the last "trapezoid" is actually just a triangle
area of trapezoids
= (1/2)(1)(6+4) + (1/2)(1)(4+2) + (1/2)(1)(2+0)
= 5 + 3 + 1
= 9
( your area consists of a triangle with a base of 3 and a height of 6
area = (1/2)base x height
= (1/2)(3)(6) = 9
If you use right endpoints for the height of each rectangle, Bob has it I think and the answer would be 8.
If you use trapezoids you get a more accurate answer, 9 , but they asked for the inaccurate answer.
To find the area under the curve of a function using right endpoints, you need to divide the interval into a certain number of strips of equal length and calculate the sum of the areas of those strips.
In this case, you are given the equation y = -2x + 6 and you want to find the area under the curve from x = 0 to x = 3 using 3 strips of equal length.
To divide the interval into 3 equal strips, you need to determine the width of each strip. The width is given by the formula (b - a) / n, where b is the upper limit of the interval, a is the lower limit of the interval, and n is the number of strips.
In this case, the lower limit is x = 0, the upper limit is x = 3, and the number of strips is 3. So the width of each strip can be calculated as (3 - 0) / 3 = 1.
Next, you need to calculate the right endpoints for each strip. Since the width of each strip is 1, the right endpoints can be obtained by adding 1 to each lower endpoint. So the right endpoints for the 3 strips are x = 1, x = 2, and x = 3.
Now, you can calculate the height of each strip by substituting the x-values of the right endpoints into the given equation y = -2x + 6. Let's calculate the heights for each strip:
- For the first strip with x = 1:
y = -2(1) + 6
= -2 + 6
= 4
- For the second strip with x = 2:
y = -2(2) + 6
= -4 + 6
= 2
- For the third strip with x = 3:
y = -2(3) + 6
= -6 + 6
= 0
Finally, to find the area under the curve, you need to calculate the area of each strip (width times height) and then sum them up:
- For the first strip with width 1 and height 4: 1 * 4 = 4
- For the second strip with width 1 and height 2: 1 * 2 = 2
- For the third strip with width 1 and height 0: 1 * 0 = 0
Adding up the areas of the three strips: 4 + 2 + 0 = 6
Therefore, the correct area under the curve of y = -2x + 6 from x = 0 to x = 3, using 3 strips of equal length using right endpoints, is 6.