Hello everyone, i'm having issues figuring out how you find the bounds of each of these graphs, I have the solution manual but I still don't see how they did it. For example: The directions say to evaluate the double integral: On the first image, for #15. THe directions say: doulbe integral D y^3 dA. D is the triangluar region with vertices (0,2) (1,1) (3,2) from (0,2) to (1,1) they got the equation of the line to be: x = 2-y; and from (1,1) to (3,2) they got x = 2y-1; So I used the line formula, y = mx + b; b is the intercept of the y-axis: m = (y1-y2)/(x1-x2); m = (1-2)/(1-3) = -1/-2 = 1/2; y = 1/2x + 2 y-2 = 1/2x x = 2y-4 They also got bounds 1 to 2 for the dy, and i'm also not sure how they came up with that either. But this isn't the answer, and also for 17, 19 and 21 i don't see how they are getting these bounds...any help would be great! For #17, i see how they get y = sqrt(4-x^2) and y = -sqrt(4-x^2) is it dy bounds becuase its in the y -axis and the dx bounds is -2 to 2 becuase in the x direction the radius is 2? but for #19 i don't see how they are getting x^4, or x, i see from (0,0) to (1,1) thats the distance of 1, so i'm guessing thats y the dx is 0 to 1?