CPM Homework Help : CALC Problem 3-91

Sketch the function f(x) = –2x² + 8x. Homework Help ✎
1. Estimate A(f, 0 ≤ x ≤ 4) using four trapezoids.
2. Write a Riemann sum representing A(f, 0 ≤ x ≤ 4) using 4 left endpoint rectangles. Then, use the summation feature of your graphing calculator to evaluate. Compare the accuracy of the trapezoids and the rectangles.
3. Will the approximation with trapezoids always equal the approximation with rectangles for all functions? Why or why not?

Hint (a):

$\text{Area of a trapezoid }=\frac{1}{2}h(b_1+b_2).$

Hint (a):

On the given domain, what will be the height of each trapezoid?

Hint (a):

The bases are determined by the function.

Hint (a):

Hint (b):

1[f(0) + f(1) + f(2) + f(3)]

Hint (c):

Think about the symmetry.

Use the eTool below to visualize this problem.
Click the link at right for the full version of the eTool: Area Under a Curve eTool