# What is the formula of anti derivative?

## What is the formula of anti derivative?

An antiderivative of a function f(x) is a function whose derivative is equal to f(x). That is, if F′(x)=f(x), then F(x) is an antiderivative of f(x).

What is an example of antiderivative?

ddx(sinx)=cosx, so F(x)=sinx is an antiderivative of cosx. Therefore, every antiderivative of cosx is of the form sinx+C for some constant C and every function of the form sinx+C is an antiderivative of cosx.

### What are the rules of Antidifferentiation?

The antiderivative rules of the six trigonometric functions are as follows:

• ∫sin x dx = -cos x + C.
• ∫cos x dx = sin x + C.
• ∫tan x dx = ln |sec x| + C.
• ∫cot x dx = ln |sin x| + C.
• ∫sec x dx = ln |sec x + tan x| + C.
• ∫csc x dx = ln |cosec x – cot x| + C.

What is the antiderivative of 2x?

The (most) general antiderivative of 2x is x2+C .

#### What is the antiderivative of COSX?

sinx
Again, people memorize that the antiderivative of cosx is sinx.

What is antiderivative in simple terms?

Antiderivatives are the opposite of derivatives. An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a function plus an arbitrary constant. Antiderivatives are a key part of indefinite integrals.

## What is the difference between integration and Antidifferentiation?

The former, (Riemann) integration, is roughly defined as the limit of sum of rectangles under a curve. On the other hand, antidifferentiation is purely defined as the process of finding a function whose derivative is given.

Are antiderivatives and integrals the same?

In additionally, we would say that a definite integral is a number which we could apply the second part of the Fundamental Theorem of Calculus; but an antiderivative is a function which we could apply the first part of the Fundamental Theorem of Calculus.

### What is the antiderivative of sin2x?

Answer: The antiderivative of sin2 x is x/ 2 – (sinx cosx) / 2.

What is the antiderivative of Sinx?

–cosx
What is the antiderivative of sin. A lot of people just memorize that the antiderivative of sinx is simply –cosx.

#### Is antiderivative same as integral?

Is anti derivative and integration same?

## How do you calculate anti – derivative?

is a simple example of a differential equation. Solving this equation means finding a function y with a derivative f. Therefore, the solutions of Equation are the antiderivatives of f. If F is one antiderivative of f, every function of the form y = F(x) + C is a solution of that differential equation.

How to find antiderivative calculator?

Write down the function. F (x) = sin (x) Interval =[,2π]

• Take the antiderivative of the function and add constant C. =∫sin(x)dx = – cos(x)+C
• Calculate the values of upper limit F (a) and lower limit F (b).
• Calculate the difference of upper limit F (a) and lower limit F (b).
• ### What is the difference between an antiderivative and an integral?

• Derivative is the result of the process differentiation, while integral is the result of the process integration. • Derivative of a function represent the slope of the curve at any given point, while integral represent the area under the curve. About the Author: Admin

How to find general antiderivative?

Find the general antiderivative of a given function.

• Explain the terms and notation used for an indefinite integral.
• State the power rule for integrals.
• Use antidifferentiation to solve simple initial-value problems.