Math 141, Spring 2016, Assignment 1

The beginner...should not be discouraged if...he finds that he does not have the prerequisites for reading the prerequisites.

- P. Halmos

State the following formulas (you do not need to prove them):

1. Formula for $\int\frac{1}{\sqrt{1-x^2}}\,dx$.
2. Formula for $\int\frac{1}{1+x^2}\,dx$.
3. Formula for $\int\tan(x)\,dx$.
4. Substitution rule.
5. Integration by parts.

Solve the following problems:

1. Section 2.7, problems 15, 17, 19, 21, and 22.
2. Section 6.1, problems 3, 7, 11, 35, 41, 43, 45, 59, and 66.
3. Copy Theorem 35 on page 193, volume 1. (Really. Copy it. This will help you to remember the formulas - and eventually you will need to remember them.)
4. Copy Theorem 45 on page 263.
5. Choose an appropriate domain restriction for the secant function, use this to define an inverse secant function, then find the derivative of the inverse secant and convert this to an integration formula. (Contrary to what I said in class, this does result in a new integration formula, one version of which appears as the third formula in Theorem 46 on page 267.)

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