Chapter 14 - Section 14.2 - Area between Two Curves and Applications - Exercises - Page 1031: 11

$4$

Here, the area can be expressed as: $A=\int_{0}^{2}[x-(-x)] \ dx=\int_{0}^{2} 2x \ dx$ In order to solve the above integral, we will use the following formula such as: $\int x^n \ dx=\dfrac{x^{n+1}}{n+1}+C$ Now, we have $\int_{0}^{2} 2x dx =[\dfrac{x^2}{2}]_{0}^{2}$ or, $=(2)^2-0$ or, $=4-0$ Therefore, the required area is: $Area=4$