# AP Calculus BC : Numerical Approximations to Definite Integrals

## Example Questions

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Explanation:

Explanation:

Explanation:

### Example Question #41 : Integrals

Approximate

using the trapezoidal rule with . Round your answer to three decimal places.

Explanation:

The interval  is 1 unit in width; the interval is divided evenly into five subintervals  units in width. They are

.

The trapezoidal rule approximates the area of the given integral  by evaluating

,

where

and

.

So

### Example Question #1 : Trapezoidal Sums

Approximate

using the trapezoidal rule with . Round your answer to three decimal places.

Explanation:

The interval  is  units in width; the interval is divided evenly into four subintervals  units in width. They are

.

The trapezoidal rule approximates the area of the given integral  by evaluating

,

where

,

,

and

.

So

### Example Question #1 : Trapezoidal Sums

Approximate

using the trapezoidal rule with . Round your estimate to three decimal places.

Explanation:

The interval  is 4 units in width; the interval is divided evenly into four subintervals  units in width - they are .

The trapezoidal rule approximates the area of the given integral  by evaluating

,

where , and

.

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