What is the integral of e^{-\theta}\cos(4\theta) d\theta? What is the integral of x^2 from x=0 to 1? what is the integral of 0? What is the integral of csc x? What is the integral of x^1 from x=4 to x=7? What is the integral of 6x + x^6?
Bjorn Poonen Integral points on curves via Baker's method and finite étale cover 47:34 Cécile Dartyge On the largest prime factor of quartic polynomial values [.] (NTW 45:36 Brian Conrey Moments, ratios, arithmetic functions in short intervals and random 50:12 David Masser Some new ...
What is the exact value of {eq}\int_0^4 e^x \,dx {/eq}? Definite Integral: The definite integral of a function {eq}f(x) {/eq} over the interval {eq}[a,b] {/eq} {eq}\displaystyle \int_{a}^{b} f(x) \; dx {/eq} ...
Using an integration formula, what is the indefinite integral \int (\cos(4x) + 2x^{2}) (\sin(4x) - x) dx? What is the integrand in the following definite integral? \int_7^9 \frac{11}{t^2} dt Integrate the following integral: integral...
Secondly, your integral is not symmetric between z1 and z2 (specifically, ∂z1). Thirdly, there is a change of order of integration. That is not always valid. Needs to be justified.Sep 19, 2012 #5 hiyok 109 0 Dear haruspex, thanks for your reply. 1. The reason why I swapped...
The expression (f(x+h)-f(x))/h to ( f(x+h)/f(x) )^(1/h) is closely related to the concept of limits in calculus. It is used to define the derivative of a function, which is the limit of (f(x+h)-f(x))/h as h approaches 0. This limit represents ...
的思想方法讲述了积分学中的基本定义,如定积分、重积分、第一型曲线曲面积分, This article adopts “the division, the approximate summation, takes the limit” the thinking method narrated in the integral calculus basic definition, like definite integral, multiple integral, first curve surface integral,[...
The substitution of some variable in the place of trigonometric ratios is known as the trigonometric substitution. We will use the trigonometric integral to evaluate the integral of the given function. Answer and Explanation:1 Given: I=∫cot(x)dxI=∫cos(x)sin(x)dx ...
(mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, th...
Another place where "dx" is often seen is in integrals. Let's focus on definite integrals. What does "dx" mean in a definite integral? "dx" here is still an infinitesimal change in x. To see why it's there, we should think of the integral as a signed area and as the limit of ...