Understanding Area Approximation Using Trapezoids

The video tutorial explains how to approximate the area under the curve y = sqrt(x - 1) from x = 1 to x = 6 using trapezoids. The process involves dividing the area into five trapezoids of equal width, calculating the area of each, and then summing them up to get an approximation. The tutorial also simplifies the expression for the area and evaluates it to find the approximate area under the curve.

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

• y = x^2 - 1

• y = sqrt(x - 1)

• y = x - 1

• y = sqrt(x)

How many trapezoids are used to approximate the area?

• Four

• Five

• Six

• Three

What is the width of each trapezoid?

• 1

• 3

• 2

• 0.5

What is the formula for the area of a trapezoid?

• Base times height

• Average of the heights times the base

• Height times width

• Sum of the bases times height

Which of the following is true about the approximation using trapezoids?

• It is an exact calculation.

• It is an overestimate.

• It is not an approximation.

• It is an underestimate.

What is the value of delta x in this approximation?

• 2

• 1

• 3

• 0.5

What is the function value at x = 1?

• 3

• 2

• 0

• 1

What is the approximate area under the curve calculated in the video?

• 9.1

• 8.0

• 7.26

• 6.5

Which tool is used to calculate the final area approximation?

• TI-85

• TI-84

• TI-86

• TI-83

What is the function value at x = 6?

• Square root of 6

• Square root of 7

• Square root of 5

• Square root of 4