Approximate the area under the curve and above the x-axis using n rectangles. Let the height of each rectangle be given
by the value of the function at the right side of the rectangle.
-$$f ( x ) = 2 x ^ { 2 } + x + 3 \text { from } x = - 2 \text { to } x = 1 ; n = 3$$
A) 25
B) 13
C) 17
D) 21

Question

Quizplus · Accepted Answer

The method described is the right Riemann sum. The interval from $x = -2$ to $x = 1$ is divided into $n = 3$ rectangles. The width ($\Delta x$) of each rectangle is $\frac{1 - (-2)}{3} = 1$. The right endpoints to evaluate the function at are $x = -1$, $x = 0$, and $x = 1$. For $x = -1$: $f(-1) = 2(-1)^2 + (-1) + 3 = 4$For $x = 0$: $f(0) = 2(0)^2 + 0 + 3 = 3$For $x = 1$: $f(1) = 2(1)^2 + 1 + 3 = 6$The approximate area is the sum of the areas of the rectangles: $Area \approx (4 + 3 + 6) \times 1 = 13$.

Approximate the Area Under the Curve and Above the X-Axis f(x)=2x2+x+3 from x=−2 to x=1;n=3f ( x ) = 2 x ^ { 2 } + x + 3 \text { from } x = - 2 \text { to } x = 1 ; n = 3f(x)=2x2+x+3 from x=−2 to x=1;n=3

Approximate the Area Under the Curve and Above the X-Axis $f ( x ) = 2 x ^ { 2 } + x + 3 \text { from } x = - 2 \text { to } x = 1 ; n = 3$