左边=∫[0--->a]dy∫[0--->y]yⁿ⁻¹f(x)dx
交换积分次序
=∫[0--->a]dx∫[x--->a]yⁿ⁻¹f(x)dy
=1/n∫[0--->a]f(x)yⁿ｜[x--->a] dx
=1/n∫[0--->a]f(x)(xⁿ-aⁿ) dx
=右边
左边=∫[0--->a]dy∫[0--->y]yⁿ⁻¹f(x)dx
交换积分次序
=∫[0--->a]dx∫[x--->a]yⁿ⁻¹f(x)dy
=1/n∫[0--->a]f(x)yⁿ｜[x--->a] dx
=1/n∫[0--->a]f(x)(xⁿ-aⁿ) dx
=右边