Thomas’ Calculus Early Transcendentals 12ed

Study Guide for Chap 05

1. Skip section 5.1.

2. Read and understand the meaning of a partition P and its norm ∥P ∥.

3. Read and understand the meaning of a Riemann sum. Practice how to express a definite integral as the limit of Riemann sum and conversely, practice how to identify a limit of Riemann sum as a definite integral.

4. Study the statement and proof of Fundamental Theorem of Calculus in both Part 1 and Part 2. Try to apply them by making up some examples to both by yourself. In particular, how to find a definite integral from antiderivative of the integrand?

5. Practice definite and indefinite integrals using substitution method. Try to make up some examples. Understand the true meaning of ’\frac{dy}{dx}dx = dy’ and how to actually use it.