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- What is an integral? - Mathematics Stack Exchange
A different type of integral, if you want to call it an integral, is a "path integral" These are actually defined by a "normal" integral (such as a Riemann integral), but path integrals do not seek to find the area under a curve I think of them as finding a weighted, total displacement along a curve
- 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
- How do I integrate $\\sec(x)$? - Mathematics Stack Exchange
My HW asks me to integrate $\sin (x)$, $\cos (x)$, $\tan (x)$, but when I get to $\sec (x)$, I'm stuck
- 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
- calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
How do you know it's legal to switch the summation and the integral? I know you can do it with finite sums but I thought there were certain conditions under which it invalid to switch them
- 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
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