What is the antiderivative of X?
What is the antiderivative of X?
That is, if F′(x)=f(x), then F(x) is an antiderivative of f(x). x33,x33+1,x33−42,x33+π. x33+c,where c is a constant….Exercise 6.
| Function | General antiderivative | Comment |
|---|---|---|
| xn | 1n+1xn+1+c | for n,c any real constants with n≠−1 |
| (ax+b)n | 1a(n+1)(ax+b)n+1+c | for a,b,c,n any real constants with a≠0, n≠−1 |
What’s the antiderivative of 1 x?
ln
The solution is quite simple: the antiderivative of 1/x is ln(|x|).
How do you find the antiderivative of F x?
Definition: General Antiderivative The function F(x) + C is the General Antiderivative of the function f(x) on an interval I if F (x) = f(x) for all x in I and C is an arbitrary constant. The function x2 + C where C is an arbitrary constant, is the General Antiderivative of 2x.
What is the antiderivative calculator?
Online integral (antiderivative) calculator is a tool that evaluates the integral of a given function with respect to a variable. It also calculates the definite as well as indefinite integral for the given function. This integral calculator also shows the steps of integration for every calculation.
What is the antiderivative of x2?
Calculus Examples By the Power Rule, the integral of x2 with respect to x is 13×3 1 3 x 3 . The answer is the antiderivative of the function f(x)=x2 f ( x ) = x 2 .
What is the antiderivative of 2 x?
Calculus Examples The integral of 2x with respect to x is 2xln(2) 2 x ln ( 2 ) . Rewrite 2xln(2)+C 2 x ln ( 2 ) + C as 1ln(2)⋅2x+C 1 ln ( 2 ) ⋅ 2 x + C . The answer is the antiderivative of the function f(x)=2x f ( x ) = 2 x .
What’s the antiderivative of Cos?
sinx
What is the antiderivative of cosx. Again, people memorize that the antiderivative of cosx is sinx.
What does it mean to say that F x is an antiderivative of f X?
A function F( x) is called an antiderivative of a function of f( x) if F′( x) = f( x) for all x in the domain of f. In other words, if F( x) and G( x) are antiderivatives of f( x) on some interval, then F′( x) = G′( x) and F( x) = G( x) + C for some constant C in the interval.
