# AP Calculus AB : Integrals

## Example Questions

Explanation:

Explanation:

Explanation:

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