Question

What is the answer of $\int\limits^a_b {x^2} \, dx$

Answer 1

Answer:

The result is:

$\dfrac{1}{3}[a^3-b^3]$

Step-by-step explanation:

Given function is:

$\displaystyle\int _b^ax^2\,dx$

Here we are using the formula of integration that has been shown below:

$\displaystyle\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+c$

Hence:

$=[\dfrac{x^3}{3}]_b^a$

$=\dfrac{1}{3}[a^3-b^3]$