The problem involves changing the bounds of integration for a double integral defined over a triangular region in the xy-plane. The original bounds are given as x going from 1 to y/2 and y from 0 to 2.
Some participants have provided guidance on clarifying the bounds and the relationships between x and y. There is a recognition of the need to express the bounds clearly to avoid confusion, particularly regarding the roles of x and y in the integration limits.
Participants are working under the constraints of a homework assignment, which may limit the information available and the methods they can use to verify their understanding.
Yes, but you're saying it in kind of a confusing way. When you say "x going from 2x to 1," you're using "x" to mean two different things. It would be better to say x goes from y/2 to 1.Kuma said:
Yes, that's right. The triangle is bounded on two sides by the x-axis and the line x=1. The third side is the line y=2x or, equivalently, x=y/2. The first form is useful when you integrate with respect to y first; the second form is useful when you integrate with respect to x first.