We have an answer to "What is the antiderivative of x2 ?"

elvishwitchxyp

Answered question

2021-12-17

What is the antiderivative of

x^{2}

Answer & Explanation

scomparve5j

Beginner2021-12-18Added 38 answers

Note that

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

n \neq - 1

amarantha41

Beginner2021-12-19Added 38 answers

The antiderivative of a function is the integral of that function. So here we have:

\int x^{2} d x

Using the rule that

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C, n \neq - 1

we that it equals:

= \frac{x^{2 + 1}}{2 + 1} + C

= {\frac{13}{x}}^{3} + C

RizerMix

Expert2021-12-29Added 656 answers

Write $x^{2}$ as a function.
$f (x) = x^{2}$
The function F(x) can be found finding the indefinite integral of the derivative $f (x)$ .
$F (x) = \int f (x) d x$
Set ip the integral to solve.
$F (x) = \int x^{2} d x$
By the power rule the integral of $x^{2}$ with respect to x is $\frac{1}{3} x^{3}$
$\frac{1}{3} x^{3} + C$
The answer is the antiderivative of the function $f (x) = x^{2}$
$F (x) = \frac{1}{3} x^{3} + C$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 1

Didn't find what you were looking for?