How do you convert an integral to a power series?
Within its interval of convergence, the integral of a power series is the sum of integrals of individual terms: ∫Σf(x)dx=Σ∫f(x)dx. See how this is used to find the integral of a power series.
What is the power rule for indefinite integrals?
Integral Rules.
| Constant Rule: | ∫kdx=kx+C. ∫ k d x = k x + C . |
|---|---|
| Sum/Difference Rule: | ∫f(x)±g(x)dx=∫f(x)dx±∫g(x ∫ f ( x ) ± g ( x ) d x = ∫ f ( x ) d x ± ∫ g ( x ) d x . |
| Power Rule: | ∫xndx=xn+1n+1+C,n≠−1. ∫ x n d x = x n + 1 n + 1 + C , n ≠ − 1 . |
| Log Rule: | ∫1xdx=ln|x|+C,x≠0. ∫ 1 x d x = ln |
What happens when you integrate power?
Recall that power is the rate work is done, or the rate at which energy is consumed or produced. In terms of current and voltage it is P=IV. It is equal to the integral of power over time. A common unit used to describe energy usage is the kilowatt-hour, the energy of 1000 W acting over one hour.
What does the indefinite integral represent?
The indefinite integral represents a family of functions whose derivatives are f. The difference between any two functions in the family is a constant. The integral key, which is used to find definite integrals, can also be used to find indefinite integrals by simply omitting the limits of integration.
What are definite and indefinite integrals?
A definite integral represents a number when the lower and upper limits are constants. The indefinite integral represents a family of functions whose derivatives are f. The difference between any two functions in the family is a constant.
What are indefinite integrals used for?
An indefinite integral is a function that takes the antiderivative of another function. It is visually represented as an integral symbol, a function, and then a dx at the end. The indefinite integral is an easier way to symbolize taking the antiderivative.