Approximate the area of the region under the function below on the interval $[ 0,2 ]$ using 8 rectangles. Round your answer to two decimals.
$$f ( x ) = \frac { 1 } { 3 } x ^ { 4 }$$
A) $5.71$ square units
B) $2.86$ square units
C) $3.69$ square units
D) $8.57$ square units
E) $17.13$ square units

Question

Quizplus · Accepted Answer

The area can be approximated using the Riemann sum with 8 rectangles. The width of each rectangle is $ \frac{2-0}{8} = 0.25 $. The height of each rectangle can be calculated using the function values at the left endpoints: $ f(0), f(0.25), f(0.5), \ldots, f(1.75) $. Summing these areas gives approximately $2.86$ square units.

Approximate the Area of the Region Under the Function Below [0,2][ 0,2 ][0,2]

Approximate the Area of the Region Under the Function Below $[ 0,2 ]$