AP Calculus AB : Integrals

Example Questions

Example Question #33 : Trapezoidal Sums      Explanation: Example Question #34 : Trapezoidal Sums      Explanation: Example Question #35 : Trapezoidal Sums      Explanation: Example Question #36 : Trapezoidal Sums      Explanation: Example Question #37 : Trapezoidal Sums

Use the trapezoidal rule to approximate the following integral:      Explanation:

The trapezoidal rule for approximating a definite integral is given by Using the above formula to approximate our integral, we get Example Question #38 : Trapezoidal Sums

Solve using the trapezoidal approximation:      Explanation:

The trapezoidal approximation of a definite integral is given by the following: Using this approximation for our integral, we get Example Question #39 : Trapezoidal Sums

Solve the integral using the trapezoidal approximation:      Explanation:

To approximate the definite integral using the trapezoidal rule, we use the following approximation: For our integral, we get Example Question #40 : Trapezoidal Sums

Approximate the integral using the trapezoidal rule:      Explanation:

To approximate the definite integral using the trapezoidal rule, we use the following approximation: For our integral, we get  Example Question #41 : Trapezoidal Sums

Using the Trapezoidal Rule with four subintervals, approximate to four decimal places:       Explanation:

The Trapezoidal Rule states that a definite integral can be approximated by computing the expression where for Since we are dividing into four subintervals, set ; the expression becomes where        Example Question #42 : Trapezoidal Sums

Solve in the integral by method of trapezoidal sums      Explanation:

To use the trapezoidal rule, we apply the following formula: Using the integral from our problem statement, we get  