Given f(x) = x³ , [2, 5]. Use the rectangle method to approximate the area using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Question

Quizplus · Accepted Answer

The width of each rectangle is (5-2)/4 = 0.75. The heights of the rectangles are f(2.375) = 13.828125, f(3.125) = 33.59375, f(3.875) = 68.90625, and f(4.625) = 125.9765625. The area of each rectangle is 0.75 * 13.828125 = 10.37109375, 0.75 * 33.59375 = 25.1953125, 0.75 * 68.90625 = 51.6796875, and 0.75 * 125.9765625 = 94.482421875. The total area is 10.37109375 + 25.1953125 + 51.6796875 + 94.482421875 = 181.728515625. The approximate area using 4 rectangles is 181.728515625/4 = 45.43212890625. The closest answer choice is A) 4.524758.

Given F(x) = X3 , [2, 5]

Given F(x) = X³ , [2, 5]