Chapter 15, Problem 44SGA

To determine

To Calculate: The given definite integral.

Answer to Problem 44SGA

  $35$

Explanation of Solution

Given:

  ${\displaystyle \underset{-3}{\overset{2}{\int }}3x^{2}dx}$

Formula Used:

  $\begin{array}{l}\text{Power Rule}:\\ {\displaystyle \int x^n}=\frac{x^{n+1}}{n+1}\end{array}$

Calculation:

  $\begin{array}{l}{\displaystyle \underset{-3}{\overset{2}{\int }}3x^{2}dx}\\ \Rightarrow 3{\left(\frac{x^{2+1}}{2+1}\right)}_{-3}^2\\ \Rightarrow 3{\left(\frac{x^3}{3}\right)}_{-3}^2\\ \Rightarrow 3\left(\frac{2^3}{3}-\frac{{\left(-3\right)}^3}{3}\right)\\ \Rightarrow 3\left(\frac{8}{3}-\left(-\frac{27}{3}\right)\right)\\ \Rightarrow 8+27\\ \Rightarrow 35\end{array}$

Conclusion:

Thus the required solution of the given integral is $35$