To graph: The function f, where f(x)=16−x2 is nonnegative and continuous on the interval [0,4].
(b)
To determine
Partition of interval [0,4] into eight subintervals of equal width and choose u as the left endpoint of each subinterval and use the partition to approximate the area under the graph of f from x=0 to x=4
(c)
To determine
Exact area of the region under the graph of f(x)=16−x2 on the interval [0,4] and compare it with approximation in part (b).
Use a change of variables to find the area of the curved rectangle above the x-axis bounded by x=4-y2/16, x=9-y2/36, x=y2/4-1, and x=y2/64-16.
Estimate the area under the graph of �(�)=�+4 over the interval [-4,-2] using eight approximating rectangles and midpoints.
Find the TOTAL geometric area bounded by the curve given by f(x) = x³ – x3
and the x-axis on the interval [-1, 1]. Sketch the graph of the function and shade the area you
found.