求平均值 y=x^2*平方根号下x^3+1 x大于等于0 小于等于2

答案是26/9 求积分,面积除以宽度2就是平均值
∫0→2 x^2√(x^3+1) dx = (1/3)∫0→2 √(x^3+1) dx^3
=(1/3)∫0→2 √(x^3+1) d(x^3+1) = (2/9)∫0→2 d(x^3+1)^(3/2)
=(2/9)[9^(3/2)-1^(3/2)] = 52/9
除以X的宽度2,得Y平均值26/9