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

3-91.

Graph the function $f(x)=−2x^2+8x$. Estimating Area Under a Curve (Desmos). Homework Help ✎

1. Approximate the area under the curve for $0\le x\le4$ using four trapezoids.

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.

$\frac{1}{2}(1)[f(0)+2(1)+2f(2) + 2f(3) + f(4)]$

2. Write a Riemann sum to approximate the area under the curve for $0\le x\le4$ using four left endpoint rectangles. Then, use the summation feature of your graphing calculator to evaluate the sum. 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?