TBIL-Cal Applications of Integration (AI)

Chapter 6 Applications of Integration (AI)

How can we use integrals to solve application questions?

By the end of this chapter, you should be able to...

Compute the average value of a function on an interval.
Estimate the arclength of a curve with Riemann sums and find an integral which computes the arclength.
Compute volumes of solids of revolution.
Compute surface areas of surfaces of revolution.
Set up integrals to solve problems involving density, mass, and center of mass.
Set up integrals to solve problems involving work.
Set up integrals to solve problems involving force and/or pressure.

Before beginning this chapter, you should be able to...

Estimate a definite integral with a Riemann sum.
- Review: Khan Academy
  ¹
  https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/generalizing-a-left-riemann-sum-with-equally-spaced-rectangles?modal=1
Evaluate the limit of a Riemann sum to find an integral.
- Review: Khan Academy
  ²
  https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/riemann-sums-and-integrals?modal=1
Solve accumulation problems with definite integrals.
- Review: Khan Academy
  ³
  https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-4/v/functions-defined-by-definite-integrals?modal=1
Find the distance between points on a curve.
- Review: Khan Academy
  ⁴
  https://www.khanacademy.org/math/geometry/hs-geo-analytic-geometry/hs-geo-distance-and-midpoints/v/distance-formula
Express the sum of indexed values using summation notation.
- Review: Khan Academy
  ⁵
  https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-3/v/sigma-notation-sum