Compute the average value of the function f(x,y) = x^2+y^2 on the diamond (square) with vertices (-1,1),(3,1),(1,-1), and (1,3). Set up the integrals and evaluate the integrals.

Evaluate the integral dx 2x 지-31x2 +C V2x+ 3 4 V3 + /2 +C 1 2/3 1/3 - V2 1 In 2/3 C. +C in(2xx-: +C A.

A right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and the third on the positive y-axis at (0, y). Express the area A of the triangle as a function of x.