### Home > CALC > Chapter 3 > Lesson 3.3.1 > Problem3-91

3-91.
1. 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?

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

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

The bases are determined by the function.

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