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Lesson Worksheet: Integration by Partial Fractions with Linear Factors Mathematics • Higher Education
In this worksheet, we will practice using partial fractions to evaluate integrals of rational functions with linear factors.
Use partial fractions to find an analytic expression for the integral
Consider the function which is defined on .
Find an antiderivative of such that . What is ?
- A, .
- B, .
- C, .
- D, .
- E, .
Is it possible to find an antiderivative that satisfies , where ? If so, what is ?
What you have found above seems to violate the result that says that any two antiderivatives must differ by a constant function, because is not a constant function. Why is there no contradiction?
- ABecause that result assumes that the domain is an interval
- BBecause is constant; it has the value 0 on and the value 1 on
- CBecause that result only holds sometimes; sometimes it fails
- DBecause neither nor is differentiable; that result only applies to differentiable functions
- EBecause that result requires additional conditions to the antiderivatives