Chapter 15
Improper Integrals and More
Approximating Techniques
T
he problems in this chapter involve improper integrals and two techniques to approximate definite integrals: Simpson’s rule and the trapezoid rule. Improper integrals are
definite integrals with limits thrown in, so those problems require you to make use of many
different calculus techniques; they can be quite challenging. The last few problems of the
chapter involve using Simpson’s rule and the trapezoid rule to approximate definite integrals. When you know the formulas for these approximating techniques, the problems are
more of an arithmetic chore than anything else.
The Problems You’ll Work On
This chapter involves the following tasks:
✓ Solving improper integrals using definite integrals and limits
✓ Using comparison to show whether an improper integral converges or diverges
✓ Approximating definite integrals using Simpson’s rule and the trapezoid rule
What to Watch Out For
Here are a few pointers to help you finish the problems in this chapter:
✓ Improper integrals involve it all: limits, l’Hôpital’s rule, and any of the integration
techniques.
✓ The formulas for Simpson’s rule and the trapezoid rule are similar, so don’t mix
them up!
✓ If you’re careful with the arithmetic on Simpson’s rule and the trapezoid rule,
you should be in good shape.
Improper Integrals and More
Approximating Techniques
T
he problems in this chapter involve improper integrals and two techniques to approximate definite integrals: Simpson’s rule and the trapezoid rule. Improper integrals are
definite integrals with limits thrown in, so those problems require you to make use of many
different calculus techniques; they can be quite challenging. The last few problems of the
chapter involve using Simpson’s rule and the trapezoid rule to approximate definite integrals. When you know the formulas for these approximating techniques, the problems are
more of an arithmetic chore than anything else.
The Problems You’ll Work On
This chapter involves the following tasks:
✓ Solving improper integrals using definite integrals and limits
✓ Using comparison to show whether an improper integral converges or diverges
✓ Approximating definite integrals using Simpson’s rule and the trapezoid rule
What to Watch Out For
Here are a few pointers to help you finish the problems in this chapter:
✓ Improper integrals involve it all: limits, l’Hôpital’s rule, and any of the integration
techniques.
✓ The formulas for Simpson’s rule and the trapezoid rule are similar, so don’t mix
them up!
✓ If you’re careful with the arithmetic on Simpson’s rule and the trapezoid rule,
you should be in good shape.