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CHAPTER
7 INTEGRATION FORMULAS LEARNING OBJECTIVES Upon completion of this chapter, you should be able to do
the following: 1. Integrate a variable to a power, a constant, a function
raised to a power, and a constant to a variable power. 2. Integrate the sum of differentiable functions, quotients,
and trigonometric functions. INTRODUCTION In this chapter several of the integration formulas and
proofs are discussed and examples are given. Some of the formulas from the
previous chapter are repeated because they are considered essential for the understanding
of integration. The formulas in this chapter are basic and should not be
considered a complete collection of integration formulas. Integration is so
complex that tables of integrals have been published as reference sources. In the following formulas and proofs, u, v, and w are considered
functions of a single variable. POWER OF A VARIABLE The integral of a variable to a power is the variable to a
power increased by one and divided by the new power. Formula.
PROOF.
Therefore,
EXAMPLE.
Evaluate
SOLUTION.*
EXAMPLE.
Evaluate
SOLUTION.^{,}
CONSTANTS A
constant may be written either before or after
the integral sign. Formula.
PROOF:
Therefore,
EXAMPLE. Evaluate
SOLUTION:
EXAMPLE: Evaluate
SOLUTION:

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