Question

Evaluate the double integral D is the triangular region with vertices \((0,0),(1,2),(0,3)\)

Short answer

The solution of the given integral can be:

Step-by-step solution

Find the limits

Consider the integral

The graph helps determine that the region is type 1.

Therefore it’s better to integrate on y first. The integrand doesn’t countermand this performance. Include the vertical line in the graph to aid in setting up the integral.

The region D is shown in the figure.

Find the equation of each boundary. The lower boundary has the equation\(y = 2x\), the upper boundary has the equation\(y = 3 - x\).

The line could slide to the left as far as\(x = 0\)and to the right as far as \(x = 1\).