The given double integral results [tex]\frac{e^8-1}{4e^8}=0.25[/tex]
Integration
The integrals are the opposite of derivatives. They are used in several applications, like: calculations of areas, volumes and others.
For solving an integration, you should know its rules. For this question will be necessary to apply the following integration rules:
- For constant function - ∫b dx = b ∫ dx= bx+C
- For integration by parts - ∫u v dx = uv -∫v du
- For exponential function - [tex]\int\ e^x \, dx[/tex] =[tex]e^x+C[/tex]
Changing the order integration
[tex]\int _0^2\int _0^xe^{-2x^2}dydx[/tex]
[tex]\int _0^2xe^{-2x^2}dx[/tex]
[tex]\frac{e^8-1}{4e^8}=0.25[/tex]
