How do you use the trapezoidal rule with n=2 to approximate the area between the curve #y=x^2# from 1 to 5?

Question

Ezra Adams · Accepted Answer

34 square units

The problem is perhaps to find the area between the given curve and the x axis, from x=1 to x=5, with two intervals. With n=2, the two intervals would be from x=1 to x=3 and from x=3 to 5. The two trapezoids so formed would have a width of two units. Sum of the area of two trapezoids would be# 1/2 *2[ f(1) +f(3) + f(3)+f(5)]# = [1+9+9+25]= 34 square units.

Christopher Agresta · Answer

undefined To use the trapezoidal rule with $ n = 2 $ to approximate the area between the curve $ y = x^2 $ from 1 to 5, you divide the interval $[1, 5]$ into two equal subintervals. Then, you find the height of each trapezoid by evaluating the function $ x^2 $ at the endpoints of each subinterval. Finally, you calculate the area of each trapezoid using the formula for the area of a trapezoid, which is $ \frac{1}{2}(b_1 + b_2)h $, where $ b_1 $ and $ b_2 $ are the lengths of the two bases and $ h $ is the height. After that, you sum up the areas of the trapezoids to get an approximation of the total area under the curve.