Help with double integral
- Thread starter arch1001
- Start date
You have two options to solve the first integral.
The first option. The hard way.
[MATH]\int_{0}^{1} \int_{1}^{9} \frac{y}{x + y^2} \ dx \ dy + \int_{1}^{3} \int_{y^2}^{9} \frac{y}{x + y^2} \ dx \ dy[/MATH]
The second option. The easy way. You can switch the variables.
[MATH]\int_{1}^{9} \int_{0}^{\sqrt{x}} \frac{y}{x + y^2} \ dy \ dx[/MATH]
Can you show us your thoughts? Why did we set the limits of integration like that? How will you solve this integral? How do you think the second integral which has triangle vertices will be solve?
The first option. The hard way.
[MATH]\int_{0}^{1} \int_{1}^{9} \frac{y}{x + y^2} \ dx \ dy + \int_{1}^{3} \int_{y^2}^{9} \frac{y}{x + y^2} \ dx \ dy[/MATH]
The second option. The easy way. You can switch the variables.
[MATH]\int_{1}^{9} \int_{0}^{\sqrt{x}} \frac{y}{x + y^2} \ dy \ dx[/MATH]
Can you show us your thoughts? Why did we set the limits of integration like that? How will you solve this integral? How do you think the second integral which has triangle vertices will be solve?