Dec 23, 2010 · One is the question of why the definite Riemann integral gives the correct notion of "area under a curve" for a (nonnegative, Riemann integrable) function. The other, which seems to be what …

For an integral of the form $$\tag {1}\int_a^ {g (x)} f (t)\,dt,$$ you would find the derivative using the chain rule. As stated above, the basic differentiation rule for integrals is:

Jul 2, 2023 · The Riemann integral follows various "intuitive" notions of area, for example if you split an interval up then the integral over the whole interval is equal to the sum of its parts, if you add two …

Jun 8, 2015 · The integral we generally teach in a first calculus course actually depends on a parameterization of the interval we are integrating over, and perhaps most naturally generalizes to …

Jul 16, 2014 · I've highlighted the part I don't understand in red. Why do we change the limits of integration here? What difference does it make? Source of Quotation: Calculus: Early …

Jun 10, 2012 · A definite integral is nothing different from an indefinite integral but the constant, that was eliminated during the differentiation, has some definite value. For instance in indefinite integrals we …

Apr 2, 2016 · The definite integral is different in the sense that it evaluates either to a number (in the single variable case) or a function independent of the variable of integration (in the multivariable case).

Just bear in mind that this is simpler than obtaining a definite integral of the Gaussian over some interval (a,b), and we still cannot obtain an antiderivative for the Gaussian expressible in terms of elementary …

Dec 4, 2020 · 2 I was finding $$\int_0^\infty e^ {-x} dx$$ So the integral becomes $$\left. (-e)^ {-x}\right\rvert_0^\infty$$ Now here's the confusing thing for me. What exactly does infinity mean in …

How to convert into a definite integral Ask Question Asked 10 years, 10 months ago Modified 8 years, 10 months ago