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- What is the integral of 1 x? - Mathematics Stack Exchange
Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers
- Integral of $\sqrt {1-x^2}$ using integration by parts
A different approach, building up from first principles, without using cos or sin to get the identity, $$\arcsin (x) = \int\frac1 {\sqrt {1-x^2}}dx$$ where the integrals is from 0 to z With the integration by parts given in previous answers, this gives the result The distance around a unit circle traveled from the y axis for a distance on the x axis = $\arcsin (x)$ $$\arcsin (x) = \int\frac
- What does it mean for an integral to be convergent?
The noun phrase "improper integral" written as $$ \int_a^\infty f (x) \, dx $$ is well defined If the appropriate limit exists, we attach the property "convergent" to that expression and use the same expression for the limit
- What is the difference between an indefinite integral and an . . .
Wolfram Mathworld says that an indefinite integral is "also called an antiderivative" This MIT page says, "The more common name for the antiderivative is the indefinite integral " One is free to define terms as you like, but it looks like at least some (and possibly most) credible sources define them to be exactly the same thing
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