Final answer:
The student is asking for the limits of integration for an iterated integral over the region R, which is a triangle. The limits are determined based on the geometry of the region, considering only the right half of the triangle as specified in the question. The correct limits for C and D, considering the upper and lower boundaries of the triangle, are 0 and 1-x, respectively.
Step-by-step explanation:
The student's question asks about setting up an iterated integral for the region R, which is a triangle with vertices −1,0),(0,1), and (1,0). The integral in question is ∫∫_R(9x+6y)²dA=∫^B_A∫^D_C(9x+6y)²dxdy. To find the correct limits of integration for A, B, C, and D, one must consider the geometry of the region R.
The bottom boundary of the triangle is the x-axis, where y=0, and the top boundary is the line connecting (1,0) to (0,1), which has an equation of y=1−x. Therefore, the limits C and D will be y=0 and y=1−x, respectively. The integral along the x-axis goes from x=-1 to x=1. However, the question specifies initial limits for A and B from 0 to 1, which suggests focusing on the right half of the triangle. Therefore, the limits for x (”c” and ”d”) should be adjusted accordingly to reflect this, with C=0 and D=1−x for this specified half.