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

3-91.

Sketch the function $f(x) =-2x^2 + 8x$.

1. Estimate $A(f, 0 ≤ x ≤ 4)$ using four trapezoids.

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

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

The bases are determined by the function.

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.

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

3. Will the approximation with trapezoids always equal the approximation with rectangles for all functions? Why or why not?