Question

Calculate the double integral of f(x,y) = 5 - 8x over the triangle with vertices 0 = (0,0), A = (3, 7), B = (5, 7).

Answer 1

To calculate the double integral of f(x,y) = 5 - 8x over the given triangle, split the triangle into smaller triangles and evaluate the double integrals over each. Then, sum up the results.

Step-by-step explanation:

To calculate the double integral of f(x,y) = 5 - 8x over the triangle with vertices 0 = (0,0), A = (3, 7), B = (5, 7), we can split the triangle into two smaller triangles. We will calculate the double integral over each triangle separately and then sum up the results.

Triangle 1: Vertices 0, A, and B

Triangle 2: Vertices 0, A, and B

By evaluating the double integrals over each triangle and adding the results, we can find the overall double integral of f(x,y) over the given triangle.