Sage-Tips

What is the antiderivative of 3 x 3?

Explanation: Well, the antiderivative of a function is the same thing as the integral of the function. So, the antiderivative of 3×3 is the same as ∫3×3 dx . We also know that x−a=1xa .

What is the antiderivative of x3?

Calculus Examples By the Power Rule, the integral of x3 with respect to x is 14×4 1 4 x 4 . The answer is the antiderivative of the function f(x)=x3 f ( x ) = x 3 .

How do you find the antiderivative of 3 x 2?

1 Answer

1. 3×2=3x−2.
2. ddxxn=nxn−1.
3. ddx1x=ddxx−1=(−1)x−2=−1×2.
4. ∫3x2dx=−3x+C.

What is the antiderivative of Cos 3x?

The antiderivative of cos 3x is ∫cos 3x dx = (1/3) sin 3x + C, where C is the constant of integration. The integration of cos 3x can be determined using the substitution method and cos 3x formula.

What’s the antiderivative of Cos?

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

Is the antiderivative of E X?

Calculus Examples The integral of ex with respect to x is ex . The answer is the antiderivative of the function f(x)=ex f ( x ) = e x .

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.

How do you find the antiderivative?

Antiderivatives are found by integrating a function. If the function in question is simple, it should be found in an antiderivative table. To find the anti-derivative of a particular function, find the function on the left-hand side of the table and find the corresponding antiderivative in the right-hand side of the table.

How to find the antiderivative?

xndx = xn+1+c as long as n does not equal -1. This is essentially the power rule for derivatives in reverse

cf (x)dx = c f (x)dx . That is,a scalar can be pulled out of the integral.

(f (x)+g(x))dx = f (x)dx+g(x)dx .

sin (x)dx = – cos (x)+c cos (x)dx = sin (x)+c sec2(x)dx = tan (x)+c These are the opposite of the trigonometric derivatives.

How do you find the integral?

The symbol for Integral is a stylish S. (for Sum, the idea of summing slices): After the Integral Symbol we put the function we want to find the integral of (called the Integrand), and then finish with dx to mean the slices go in the x direction (and approach zero in width).

What is anti – derivative?

An anti-derivative is basically an integral, which is the second main concept of calculus. When doing a derivative you take away a power, when doing an anti-derivative, you add a power, in otherwords it undoes whatever a derivative does.