Chapter 8.5, Problem 4QR

To determine

To find the value of the integral ${\displaystyle \underset{0}{\overset{3}{\int }}\left(x^2+2\right)dx}$ by finding the anti-derivative.

Answer to Problem 4QR

The value of the integral is 15.

Explanation of Solution

Given information: ${\displaystyle \underset{0}{\overset{3}{\int }}\left(x^2+2\right)dx}$

Formula used: ${\displaystyle \int x^{n}dx}=\frac{x^{n+1}}{n+1}+C$

Calculation :

The given integral is

  ${\displaystyle \underset{0}{\overset{3}{\int }}\left(x^2+2\right)dx}={\left[\frac{x^3}{3}+2x\right]}_0^3=9+6=15$

Hence, the value of the integral is 15.