Answer:
![A = [(32)/(3)]](https://img.qammunity.org/2021/formulas/mathematics/college/r4ixy24ylspcap3777avgrwg46exex35nh.png)
Explanation:
Given


Required
Determine the area bounded by the curves
First, we need to determine their points of intersection

Subtract 2x from both sides

Multiply through by -1

Take square root of both sides
or

This Area is then calculated as thus
![A = \int\limits^a_b {[y_1 - y_2]} \, dx](https://img.qammunity.org/2021/formulas/mathematics/college/8lzvgcxc9mnlc1mi4vjcrooujr84urtr0e.png)
Where a = 2 and b = -2
Substitute values for
and


Open Brackets

Collect Like Terms


Integrate
](https://img.qammunity.org/2021/formulas/mathematics/college/dxta0mvpnz2xj8s6mdg7gwt6si12bc88e7.png)
![A = [-(2^(3))/(3) +4(2)] - [-(-2^(3))/(3) +4(-2)]](https://img.qammunity.org/2021/formulas/mathematics/college/bpqhu687mkrod9njms9fxtwyss72j5yn7k.png)
![A = [-(8)/(3) +8] - [-(-8)/(3) -8]](https://img.qammunity.org/2021/formulas/mathematics/college/8ywkycus48z7foun77whjzto7rjio838oq.png)
![A = [(-8+ 24)/(3)] - [(8)/(3) -8]](https://img.qammunity.org/2021/formulas/mathematics/college/rfqb5s5m33rz8adjp9ifrwqrrv5q2wuccx.png)
![A = [(-8+ 24)/(3)] - [(8-24)/(3)]](https://img.qammunity.org/2021/formulas/mathematics/college/rivbo1p8jo99nmju6q75lmatzamu73lxzv.png)
![A = [(16)/(3)] - [(-16)/(3)]](https://img.qammunity.org/2021/formulas/mathematics/college/cgwxm3n2uwmfrt0xiit7y8vzm0y4o3myov.png)
![A = [(16)/(3)] + [(16)/(3)]](https://img.qammunity.org/2021/formulas/mathematics/college/648ezhcqqtsc7l5mln84fxc98dumkwwk6o.png)
![A = [(16 + 16)/(3)]](https://img.qammunity.org/2021/formulas/mathematics/college/f4hgf24d0bsx8gim5rdgdvoqkk8gx4q6y9.png)
![A = [(32)/(3)]](https://img.qammunity.org/2021/formulas/mathematics/college/r4ixy24ylspcap3777avgrwg46exex35nh.png)
Hence, the Area is:
![A = [(32)/(3)]](https://img.qammunity.org/2021/formulas/mathematics/college/r4ixy24ylspcap3777avgrwg46exex35nh.png)