Approximating Area Under a Curve

What is the primary purpose of using Riemann sums in numerical integration?

• To approximate the area under a curve

• To find the exact value of an integral

• To solve differential equations

• To calculate the derivative of a function

CALCULATOR PERMITTED

• A

• B

• C

• D

• E

• A
• B
• C
• D

• A
• B
• C
• D

• 1.5

• 1.1418

• 1.1

• 1.4914

What is the approximate area under the curve, using 4 intervals with heights using left values?

• 20

• 14

• 10

• 8

• 35

• 40.625

• 32.1

• 41

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

• Overestimate

• Underestimate

• Exact Solution

• Unable to Determine

What does this picture represent?

• Left Riemann Sum

• Middle Riemann Sum

• Right Riemann Sum

• Trapezoidal Sum

Which method is commonly used to approximate the area under a curve when the function is difficult to integrate analytically?

• Trapezoidal Rule

• Simpson's Rule

• Monte Carlo Integration

• All of the above