for the following graph of a function, estimate the area under the curve on the interval -5, -2 using the…

for the following graph of a function, estimate the area under the curve on the interval -5, -2 using the right - endpoint approximation and 3 rectangles.

for the following graph of a function, estimate the area under the curve on the interval -5, -2 using the right - endpoint approximation and 3 rectangles.

Answer

Explanation:

Step1: Calculate width of rectangles

The interval is $[-5,-2]$, and $n = 3$. The width $\Delta x=\frac{b - a}{n}=\frac{-2-(-5)}{3}=\frac{-2 + 5}{3}=1$.

Step2: Identify right - endpoints

The right - endpoints of the three sub - intervals $[-5,-4],[-4,-3],[-3,-2]$ are $x_1=-4,x_2=-3,x_3=-2$.

Step3: Estimate function values at right - endpoints

From the graph, $f(-4)\approx 2$, $f(-3)\approx 1$, $f(-2)\approx 4$.

Step4: Calculate area of each rectangle and sum

The area of a rectangle is $A = f(x_i)\Delta x$. The sum of the areas of the three rectangles $A\approx f(-4)\Delta x+f(-3)\Delta x+f(-2)\Delta x=(2\times1)+(1\times1)+(4\times1)=2 + 1+4 = 7$.

Answer:

7