Chapter 6.4, Problem 42E

To determine

To find the area of the region between the given curve and x-axis.

Answer to Problem 42E

4.

Explanation of Solution

Given:

  $y=3x^2-3,-2\le x\le 2$

Calculation:

Required area is,

  $\begin{array}{l}{\displaystyle \underset{-2}{\overset{2}{\int }}ydx}={\displaystyle \underset{-2}{\overset{2}{\int }}\left(3x^2-3\right)dx}\\ ={\left[3\cdot \frac{x^3}{3}-3x\right]}_{-2}^2\\ ={\left[x^3-3x\right]}_{-2}^2\\ =\left[{\left(2\right)}^3-3\left(2\right)\right]-\left[{\left(-2\right)}^3-3\left(-2\right)\right]\\ =2+2\\ =4\end{array}$