Chapter 4.4 - The Fundamental Theorem of Calculus

Objectives:

• • Evaluate a definite integral using the Fundamental Theorem of Calculus.

  • Understand and use the Mean Value Theorem for Integrals.

  • Find the average value of a function over a closed interval.

  • Understand and use the Second Fundamental Theorem of Calculus.

Fundamental Theorem of Calculus pt1 (for Day #41 lesson)

Introduction to using the FTC to evaluate definite integrals.

(FYI This video was recorded months earlier than most of the others, so that's why it looks a bit different).

Fundamental Theorem of Calculus pt2 (for Day #42 lesson)

Given multiple equations, write the definite integral representing the area of the region bounded by the graphs. Then use the FTC to evaluate the integrals.

MVT for Integrals & Second FTC (for Day #43 lesson)

View the Mean Value Theorem through the lens of integral Calculus. Also, applying the Second Fundamental Theorem of Calculus.

The video does not include a 2nd FTC example requiring the Chain Rule. Here are a couple Second FTC written examples that may provide some further insight.

Format/Topics of Chapter 4.4 Assessment

Remember, this test does not cover all of Chapter 4.4. It only goes through the (first) FTC. Note that this test will NOT include 2nd FTC or MVT for integrals.

15 Multiple Choice

• • All topics are fair game, as usual

10 Free Response

• • Area under curve using the limit/summation definition, i.e. limΣ(base)(height). FTC not allowed.

  • Definite integral via geometric formula

  • FTC (rewriting necessary)

  • Properties of Integrals

  • Definite Integrals in which you have to find the limits of integration

  • Average Value and MVT for Integrals

  • 2nd FTC