# How Do You Find The Antiderivative Of A Table?

What is the easiest way to find the antiderivative?

How do you find the antiderivative for a function?

To find an antiderivative for a function f, we can often reverse the process of differentiation. For example, if f = x4, then an antiderivative of f is F = x5, which can be found by reversing the power rule. Notice that not only is x5 an antiderivative of f, but so are x5 + 4, x5 + 6, etc.

What is the formula for Antiderivatives?

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). 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

## Related Question How do you find the Antiderivative of a table?

### How do you find the antiderivative of U substitution?

• Set u equal to the argument of the main function.
• Take the derivative of u with respect to x.
• Solve for dx.
• Make the substitutions.
• Antidifferentiate by using the simple reverse rule.
• Substitute x-squared back in for u — coming full circle.
• ### Is the antiderivative the same as the integral?

Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

### What is antiderivative of Secx?

The antiderivative of sec x is mathematically writen as ∫ sec x dx. Multiply and divide sec x by (sec x + tan x), we get, ∫ sec x dx = ∫ sec x · (sec x + tan x) / (sec x + tan x) dx = ∫ (sec2x + sec x tan x) / (sec x + tan x) dx.

### What is an antiderivative of a function give an example?

Example: F(x)=x3 is an antiderivative of f(x)=3x2. Also, x3+7 is an anti-derivative of 3x2, since d(x3)dx=3x2 and d(x3+7)dx=3x2. The most general antiderivative of f is F(x)=x3+C, where c is an arbitrary constant.

### What's the Antiderivative of tan?

The integral of tan x is ln|cos x| + C .

### How do you find the antiderivative of a sine function?

The general antiderivative of sin(x) is −cos(x)+C . With an integral sign, this is written: ∫sin(x) dx=−cos(x)+C .

### How do you find the antiderivative of sin?

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

### What is the antiderivative of Sec 2?

and the general antiderivative of sec2x is tanx+C .

### What is Sinx integration?

The integral of sin x is -cos x + C. It is mathematically written as ∫ sin x dx = -cos x + C.

### How do you know when to use U substitution?

Always do a u-sub if you can; if you cannot, consider integration by parts. A u-sub can be done whenever you have something containing a function (we'll call this g), and that something is multiplied by the derivative of g. That is, if you have ∫f(g(x))g′(x)dx, use a u-sub.

### How integration is antiderivative?

Indefinite integral means integrating a function without any limit but in definite integral there are upper and lower limits, in the other words we called that the interval of integration. The antiderivative of x² is F(x) = ⅓ x³. The definite integral, however, is ∫ x² dx from a to b = F(b) – F(a) = ⅓ (b³ – a³).

### What are Antiderivatives used for?

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 does it mean for a function f to be an antiderivative of a function f on an interval I?

Definition A function F is called an. antiderivative of f on an interval I if F (x) = f (x) for all x in I. Example Let f (x) = x2. Then an antiderivative. F(x) for x2 is F(x) = x3.

### What is the antiderivative of cot?

The integral of cot x is ln |sin x| + C.

### What is the antiderivative of CSC?

The antiderivative of csc2x is −cotx+C .

### What are the integration rules?

Integration Rules

Common Functions Function Integral
Power Rule (n≠−1) ∫xn dx xn+1n+1 + C
Sum Rule ∫(f + g) dx ∫f dx + ∫g dx
Difference Rule ∫(f - g) dx ∫f dx - ∫g dx
Integration by Parts See Integration by Parts

### What is the Antiderivative of TANX Secx?

What is the Anti-derivative of Sec x Tan x? The anti-derivative of sec x tan x is equal to sec x + C, where C is the constant of integration.

### What is the Antiderivative of sin 2x?

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

### What is integral of constant?

The integral of a constant is calculating the area under a horizontal line at y = a, where is some constant. There for given a definite integral it would simply be a rectangular box with a length of a, and a width of c-b, where the bounds wiuld be [b,c].

### Why is the Antiderivative of sin?

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