Approximating Area Under a Curve Using Rectangles

The video tutorial explains how to approximate the area under the function f(x) = 4/x on the interval from 1 to 5 using eight left-sided rectangles. The process involves dividing the interval into eight equal parts, calculating the height of each rectangle using the left side of the interval, and summing the areas of these rectangles to approximate the total area under the curve. The tutorial also demonstrates using a calculator to perform these calculations efficiently, resulting in an approximate area of 4,609/630. The video concludes by mentioning the next step of using right-sided rectangles for the same problem.

What is the function used to approximate the area under the curve?

• f(x) = x^4

• f(x) = x/4

• f(x) = 4/x

• f(x) = 4x

How many equal intervals is the interval from 1 to 5 divided into?

• Six

• Eight

• Ten

• Four

What is the width of each rectangle used in the approximation?

• 1 unit

• 1/2 unit

• 1/4 unit

• 2 units

Which point is used to determine the height of each rectangle?

• Any point

• Right endpoint

• Midpoint

• Left endpoint

What is the term used to describe the sum of the areas of the rectangles?

• Exact sum

• Midpoint sum

• Upper sum

• Lower sum

What tool is suggested for calculating the sum of the areas of the rectangles?

• Calculator

• Graph paper

• Ruler

• Protractor

What is the function notation used in the calculator for this problem?

• Y1

• F1

• H1

• G1

What is the approximate area under the curve using eight left-sided rectangles?

• 5,000/700

• 3,000/500

• 4,609/630

• 2,500/400

What is the next method mentioned for approximating the area under the curve?

• Using midpoints

• Using trapezoids

• Using right-sided rectangles

• Using circles

Why is it not recommended to calculate the area by hand?

• It is too simple

• It is too complex

• It is too expensive

• It is too inaccurate