Use the limit process to find the area of the region between the graph of the function and the x-axis over the specified interval.
$\begin{array} {l }
\text {Function }& \text {Interval }\
f ( x ) = x ^ { 2 } + 2&[0,1]\
\end{array}$
A)A = 2 square units
B)A = 3.33 square units
C)A = 3 square units
D)A = 2.33 square units
E)A = 2.67 square units

Question

Use the limit process to find the area of the region between the graph of the function and the x-axis over the specified interval.
 $\begin{array} {l } 
 \text {Function }& \text {Interval }\
f ( x ) = x ^ { 2 } + 2&[0,1]\
\end{array}$ 
A)A = 2 square units
B)A = 3.33 square units
C)A = 3 square units
D)A = 2.33 square units
E)A = 2.67 square units

Quizplus · Accepted Answer

The area under the curve $ f(x) = x^2 + 2 $ from $ x = 0 $ to $ x = 1 $ is calculated using the definite integral: $\int_{0}^{1} (x^2 + 2) \, dx = \left[\frac{x^3}{3} + 2x\right]_{0}^{1} = \frac{1}{3} + 2 = \frac{7}{3} = 2.33$ square units.

Use the Limit Process to Find the Area of the Region