Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles).

Question

Approximate the area under the curve defined by the function  over the interval x = 0 to x = 3 using the right-hand endpoints of three subintervals (rectangles). ​

Quizplus · Accepted Answer

Dividing the interval [0,3] into three subintervals of equal width, we have $\Delta x = \frac{3-0}{3} = 1$. Using right-hand endpoints, the three rectangles have heights $f(1), f(2),$ and $f(3)$, respectively. Therefore, the approximate area is:

$\Delta A \approx f(1) \Delta x + f(2) \Delta x + f(3) \Delta x$

$= f(1) + f(2) + f(3)$

$= e^1 + e^2 + e^3 \approx \boxed{24.54}$

The closest choice is B with a value of 24.535.

Approximate the Area Under the Curve Defined by the Function