AP Calculus AB : Integrals

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

Example Question #33 : Trapezoidal Sums

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Example Question #34 : Trapezoidal Sums

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Example Question #35 : Trapezoidal Sums

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Example Question #36 : Trapezoidal Sums

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Example Question #37 : Trapezoidal Sums

Use the trapezoidal rule to approximate the following integral:

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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:

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Correct answer:

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:

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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:

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Correct answer:

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:

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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

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Correct answer:

Explanation:

To use the trapezoidal rule, we apply the following formula:

Using the integral from our problem statement, we get

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